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Processus ponctuels

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Book cover Ecole d’Eté de Probabilités de Saint-Flour VI-1976

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Bibliographie

  • ACQUAVIVA A. Théorème de relèvement et répartitions ponctuelles à points distincts en nombre localement fini. C.R. Acad. Sci. Paris 281 (1975) 297–300

    MathSciNet  MATH  Google Scholar 

  • ADAMOPOULOS L. Some counting and interval properties of the mutually-exciting processes J. Appl. Proba. 12 (1975) 78–86

    Article  MathSciNet  MATH  Google Scholar 

  • AMBARTZUMIAN R.V. Correlation properties of the intervals in the superpositions of independent stationary recurrent point processes. Studia Sci. Hung 4 (1969) 161–170

    MathSciNet  Google Scholar 

  • Random plane mosaics. Dokl Akad Nauk SSSR 200 (1971) 255–258; Soviet Math Dokl 12 (1971) 1349–1353

    MathSciNet  Google Scholar 

  • Palm distributions and superpositions of independent point processes in Rn. Stochastic point processes. PAW Lewis Ed. Wiley (1972) 626–645

    Google Scholar 

  • The solution of the Buffon-Sylvester problem in R3. ZfW 27 (1973) 53–74

    MathSciNet  MATH  Google Scholar 

  • AMBROSE W. Representation of ergodic flows. Ann. Math 42 (1941) 723–739

    Article  MathSciNet  MATH  Google Scholar 

  • AMBROSE W. et KAKUTANI S. Structure and continuity of measurable flows. Duke Math J. 9 (1942) 25–42

    Article  MathSciNet  MATH  Google Scholar 

  • AMBROSE W., HALMOS P.R. et KAKUTANI S. Decomposition of measures. Duke Math J. 9 (1942) 43–47

    Article  MathSciNet  MATH  Google Scholar 

  • BARTLETT M.S. An introduction to stochastic processes. Cambridge Univ. Press (1966) 2ème édition.

    Google Scholar 

  • BENÈS V.E. General stochastic processes in the theory of queues. Addison — Wesley Mass. 1963

    Google Scholar 

  • BENVENISTE A. Processus stationnaires et mesures de Palm du flot spécial sous une fonction. Thèse Paris.

    Google Scholar 

  • BENVENISTE A. et JACOD J. Intensité stochastique d’un processus ponctuel stationnaire, reconstruction du processus ponctuel à partir de son intensité stochastique C.R. Acad. Sci.Paris 280 (1975) 821–5

    MathSciNet  MATH  Google Scholar 

  • BEUTLER F.J. et LENEMAN OAZ The theory of stationary point processes. Acta Math. 116 (1966) 159–197

    Article  MathSciNet  MATH  Google Scholar 

  • BILLINGSLEY P. Convergence of probability measures. Wiley (1968)

    Google Scholar 

  • BLANCHARD F. Processus de points marqués et processus ramifiés. Ann. IHP 9 (1973) 259–276

    MathSciNet  MATH  Google Scholar 

  • BOEL R., VARAYIA P. et WONG E. Martingales of jump processes, I and II. Siam J. Control 13 (1975) 999–1061

    Article  MathSciNet  MATH  Google Scholar 

  • BOROVKOV A.A. On the first passage time for a class of processes with independent increments. Teor. Veraj. Prim. 10 (1965) 360–364

    MathSciNet  MATH  Google Scholar 

  • Some limit theorems in queuing theory. Teor. Veroj. Prim. 9 (1984) 608–625; 10 (1965) 409–437

    MathSciNet  MATH  Google Scholar 

  • Asymptotic analysis of some queuing systems. Teor. Veroj. Prim. 11 (1966) 675–682

    MathSciNet  MATH  Google Scholar 

  • Stochastic processes in queuing theory. Springer (1976)

    Google Scholar 

  • BREIMAN L. The Poisson tendency in traffic distribution. Ann. Math. Stat. 34 (1963) 308–311

    Article  MathSciNet  MATH  Google Scholar 

  • BREMAUD P. The martingale theory of point processes over the real half-line admitting an intensity. Proc. IRIA Conf., Lect. Notes Op. Res. and Math. Systems, Springer 107 (1974) 519–542.

    Article  MathSciNet  Google Scholar 

  • An extension of Watanabe’s theorem of characterization of Poisson processes over the positive real half line. J. Appl. Prob. 12 (1975) 396–399

    Article  MathSciNet  MATH  Google Scholar 

  • Estimation de l’état d’une file d’attente et du temps de panne d’une machine par la méthode des semi-martingales. Adv. Appl. Proba. 7 (1975)

    Google Scholar 

  • On the information carried by a stochastic point process. Revue Cethedec 43 (1975)

    Google Scholar 

  • Bang-Bang controls of point processes. Adv. Appl. Proba 8 (1976) 385–394

    Article  MathSciNet  MATH  Google Scholar 

  • BREMAUD P. et JACOD J. Processus ponctuels et martingales

    Google Scholar 

  • BRILLINGER D. The identification of point process systems. Ann. Proba 3 (1976) 909–929

    Article  MathSciNet  MATH  Google Scholar 

  • BROWN M. Sampling with random jitter. J. Soc. Ind. Appl. Math. 11 (1963) 460–473

    Article  MathSciNet  MATH  Google Scholar 

  • [2] An invariance property of Poisson processes. J. Appl. Proba 6 (1969) 453–458

    Article  MathSciNet  MATH  Google Scholar 

  • A property of Poisson processes and its applications to macroscopic equilibrum of particle systems. Ann. Math. Stat. 41 (1970) 1935–41

    Article  MATH  Google Scholar 

  • Discrimination of point processes. Ann. Math. Stat. 42 (1971)

    Google Scholar 

  • CARTER D.S. et PRENTER P.M. Exponential spaces and counting processes. ZfW 21 (1972) 1–19

    MathSciNet  MATH  Google Scholar 

  • CHOQUET G. Theory of capacities. Ann. Fourier 5 (1953) 131–295

    Article  MathSciNet  MATH  Google Scholar 

  • CHOU C.S. et MEYER P.A. Représentation des martingales comme intégrales stochastiques dans les processus ponctuels. C.R. Acad. Sci. Paris A 278 (1974) 1561–3

    MathSciNet  Google Scholar 

  • CHIMG K.L. Crudely stationary counting processes. Amer. Math. Monthly 79 (1972) 867–877

    Article  MathSciNet  MATH  Google Scholar 

  • CINLAR E. Superposition of point processes. Stochastic point processes, P. Lewis Ed., Wiley (1972) 549–606

    Google Scholar 

  • COHEN J.W. The single server queue. North-Holland, Amsterdam 1969

    MATH  Google Scholar 

  • Asymptotic relations in queuing theory. Stoch. Prob. Appli 1 (1973) 107–124

    Article  MATH  Google Scholar 

  • COX D.R. Renewal theory. Methuen’s monograph, London 1962

    MATH  Google Scholar 

  • COX D.R. et LEWIS P.A.W. The statistical Analysis of series of Events. Methuen, London (1966); Trad. fr. Dunod 1969

    Book  MATH  Google Scholar 

  • Multivariate point processes. Proc. 6th Berkeley Symp 3 (1972) 401–425

    MathSciNet  MATH  Google Scholar 

  • CRAMER H. et LEADBETTER M.R. Stationary and related stochastic processes. Wiley (1967)

    Google Scholar 

  • CRAMER H., LEADBETTER M.R. et SERFLING On distribution function moment relationships in a stationary point process. ZfW 18 (1971) 1–8

    MathSciNet  MATH  Google Scholar 

  • DALEY D.J. The correlation structure of the output process of some single server queuing systems. Ann. Math. Stat 39 (1968) 1007–19

    Article  MathSciNet  MATH  Google Scholar 

  • Asymptotic properties of stationary point processes with generalized clusters. ZfW 21 (1972) 65–76

    MathSciNet  MATH  Google Scholar 

  • Markovian processes whose jump epochs constitute a renewal process Quart. J. Math. Oxford 24 (1973) 97–105

    Article  MathSciNet  MATH  Google Scholar 

  • Poisson and alternating renewal processes with superposition a renewal process. Math. Nachr 57 (1973) 359–369

    Article  MathSciNet  MATH  Google Scholar 

  • Various concepts of orderliness for point-processes. Stochastic Geometry, Wiley (1974), 148–161

    Google Scholar 

  • Queuing output processes. Adv. Appl. Proba 8 (1976) 395–415

    Article  MathSciNet  MATH  Google Scholar 

  • DALEY D.J. et MILNE R.K. Orderliness, intensities and Palm-Khinchin equations for multivariate processes. J. Appl. Proba. 12 (1975) 383–389

    Article  MathSciNet  MATH  Google Scholar 

  • DALEY D.J. et OAKES D. Random walk point processes. ZfW 30 (1974) 1–16

    MathSciNet  MATH  Google Scholar 

  • DALEY D.J. et VERE-JONES D. A summary of the theory of point processes. Stochastic point processes, P. Lewis Ed. Wiley (1972) 299–383

    Google Scholar 

  • DAVIDSON R. Some arithmetic and geometry in probability theory. Thesis Cambridge 1968. Stochastic geometry, a memorial volume, Wiley 1974.

    Google Scholar 

  • DAVIS M.H.A. et ELLIOTT R.J. Representation of martingales of jump processes. Siam J. Control (1976)

    Google Scholar 

  • DAVIS M.H.A. et Optimal control of a jump process (1975)

    Google Scholar 

  • DAVIS M.H.A., KAILATH T. et SEGALL A. Non-linear filtering with counting observations. IEEE II 21 (1975) 143–150

    MathSciNet  MATH  Google Scholar 

  • DEBES H., KERSTAN J., LIEMANT A. et MATTHES K. Verallgemeinerung eines Satzes von Dobrušin. Math Nachrichten 47 (1970) 183–244, 50 (1971) 99–139 et 51 (1971) 149–188.

    Article  MathSciNet  MATH  Google Scholar 

  • DELLACHERIE C. Capacités et processus stochastiques. Springer 1972

    Google Scholar 

  • Intégrales stochastiques par rapport aux processus de Wiener et de Poisson. Sem. Proba. Strasbourg, Lect. Notes Math 381 (1974) 25–26 et 465 (1975) 494

    Article  MathSciNet  Google Scholar 

  • DELLACHERIE C. et MEYER P.A. Probabilités et Potentiel, Hermann (1976)

    Google Scholar 

  • DISNEY R.L. et CHERRY W.P. Some topics in queuing network theory. Proc. Conf. Western Michigan Univ 1973. Lecture Notes in Economics 98, 23–44

    Google Scholar 

  • DOLEANS-DADE C. Quelques applications de la formule de changement de variables pour les semi-martingales. ZfW 16 (1970) 181–194

    MATH  Google Scholar 

  • Existence and Unicity of stochastic integral equations. ZfW 36 (1976) 93–101

    MathSciNet  MATH  Google Scholar 

  • DOLEANS-DADE C. et MEYER P.A. Intégrales stochastiques par rapport aux martingales locales. Sém. de Proba, Strasbourg 4, Lecture Notes Springer 124 (1970) 77–107

    MATH  Google Scholar 

  • DRISCOLL M.F. et WEISS N.A. Random translations of stationary point processes. J. Math. Anal. Appl. 48 (1974) 423–433

    Article  MathSciNet  MATH  Google Scholar 

  • ELKAROUI N. et LEPELTIER J.P. Représentation des processus ponctuels multivariés à l’aide de processus de Poisson. C.R. Acad. Sci. Paris A (1975)

    Google Scholar 

  • ELLIOTT R.J. Stochastic integrals for martingales of a jump process. Report Hull Univ.

    Google Scholar 

  • Martingales of a jump process with partially accessible jump times. Report Hull Univ.

    Google Scholar 

  • Levy systems and absolutely continuous changes of measures for a jump process. Report Hull Univ.

    Google Scholar 

  • Levy functionals and jump process martingales. Report Hull Univ.

    Google Scholar 

  • Innovation projections of a jump process and local martingales. Report Hull Univ.

    Google Scholar 

  • FELLER W. An introduction to probability and its applications. Vol. 1 and 2. Wiley

    Google Scholar 

  • FICHTNER K.H. Charakterisierung Poissonscher zufülliger Punktfolgen und infinitesimale Verdünnungsschemata. Math. Nachr 68 (1975) 93–104

    Article  MathSciNet  MATH  Google Scholar 

  • FIEGER W. Zwer Verallgemeinerungen der Palmschen Formeln. Trans. 3nd Prague Conf (1964), 107–122

    Google Scholar 

  • Eine für beliebige Call-Prozesse geltende Verallgemernerung der Palmschen Formeln. Math. Scan 16 (1965) 121–147

    MathSciNet  MATH  Google Scholar 

  • Die Anzahl der γ-niveau Kreuzungspunkte von stochastischen Prozessen ZfW 18 (1971) 227–260

    MathSciNet  MATH  Google Scholar 

  • FISCHER L. A survey of the math theory of multi-dimensional point processes. Stochastic point processes, PAW Lewis ed. Wiley (1972) 468–513

    Google Scholar 

  • FORTET R. Sur les répartitions ponctuelles aléatoires. Ann IHP 4 (1968) 99–112

    MathSciNet  MATH  Google Scholar 

  • Définition et lois de probabilité des répartitions ponctuelles aléatoires. Zastosowania Matematyki 10 (1969) 57–73

    MathSciNet  MATH  Google Scholar 

  • FORTET R. et KAMBOUZIA M. Lois de probabilité des répartitions ponctuelles markoviennes et des répartitions ponctuelles cumulatives. CR. Acad. Sci. 268 (1969) 644–5

    MathSciNet  MATH  Google Scholar 

  • Recouvrement par un ensemble aléatoire. CR. Acad. Sci. 281 (1975) 397–8

    MathSciNet  MATH  Google Scholar 

  • Ensembles aléatoires induits par une répartition ponctuelle aléatoire CR. Acad. Sci. 280 (1975) 1447–50

    MathSciNet  MATH  Google Scholar 

  • FRANKEN P. Approximation durch Poissonsche Prozesse. Math Nachr 26 (1963) 101–114

    Article  MathSciNet  MATH  Google Scholar 

  • FRANKEN P., LIEMANT A. et MATTHES K. Stationäre zufällige Puntkfolgen I–III. J.Ber Deutsch Math Verein 65 (1963) 66–79, 66 (1964) 106–118 et 67 (1965) 183–202.

    MATH  Google Scholar 

  • FRIEDMAN N.A. Introduction to Ergodic theory. Van Nostrand (1970)

    Google Scholar 

  • FRISCH H.L. et HAMMERSLEY J.M. Percolation processes and related topics. J. Soc. Ind. Appl. Math II (1963) 894–918

    Google Scholar 

  • FUJISAKI M., KALLIANPUR G. et KURITA H. Stochastic differential equations for the non-linear filtering problem Osaka J. Math 9 (1972) 19–40

    MathSciNet  MATH  Google Scholar 

  • FURSTENBERG H. et TZKONI I. Spherical functions and integral geometry. J. Israel Math 10 (1971) 327–338

    Article  MathSciNet  MATH  Google Scholar 

  • GEMAN D. Horizontal-window conditioning and the zeros of stationary processes

    Google Scholar 

  • On the variance of the number of zeros of a stationary Gaussian process. Ann. Math. Stat.

    Google Scholar 

  • GEMAN D. et HOROWITZ J. Remarks on Palm measures. Ann IHP 9 (1973) 215–232

    MathSciNet  MATH  Google Scholar 

  • Random shifts which preserve measure. Proc AMS 49 (1975) 143–150

    Article  MathSciNet  MATH  Google Scholar 

  • Polar sets and Palm measures in the theory of flows. Trans AMS 208 (1975) 141–159

    Article  MathSciNet  MATH  Google Scholar 

  • Time conditionning of random processes

    Google Scholar 

  • Transformation of flows by discrete random measures. Indiana J. Math 24 (1975) 291–306

    Article  MathSciNet  MATH  Google Scholar 

  • GIGER et HADWIGER Uber Treffzahlwahrscheinlickkeiten in Eikörperfeld. ZfW 10 (1968) 329–334

    MathSciNet  MATH  Google Scholar 

  • GIRSANOV I. On transforming a certain class of stochastic processes by absolutely continnous substitution of measures. Teor. Veroj i Prim. 5 (1960) 285–301

    MATH  Google Scholar 

  • GNEDENKO B.V. et KOVALENKO I.N. Introduction to queuing theory. Nauka, Moscou (1966). Trad. anglaise Jesuralem (1968)

    Google Scholar 

  • HINCIN A Ya (ou KHINTCHINE) On Poisson streams of random events. Teor. Veroj. 1 (1956) 320–7; Th. Proba. 1 (1956) 291–7

    Google Scholar 

  • HOFFMAN-JORGENSEN J. Markov sets. Math. Scand. 24 (1969) 145–166

    MathSciNet  Google Scholar 

  • ISHAM V. On a point process with independent locations. J. Appl. Proba. 12 (1975) 435–446

    Article  MathSciNet  MATH  Google Scholar 

  • ITO K. Poisson point processes attached to Markov processes. Proc. 6th Berkeley Symp (1972) III, 225–239

    MathSciNet  MATH  Google Scholar 

  • JACOD J. Two dependent Poisson processes whose sum is still a Poisson process. J. Appl. Proba 12 (1974) 1–12

    MathSciNet  Google Scholar 

  • Multivariate point processes: predictable projection, Radon-Nikodym derivatives, representation of martingales. Z.f.W. 31 (1975) 235–253

    Article  MathSciNet  MATH  Google Scholar 

  • Un théorème de représentation pour les martingales discontinues. Z.f.W. 34 (1976) 225–244

    Article  MathSciNet  MATH  Google Scholar 

  • JACOD J. et MEMIN J. Caractéristiques locales et conditions de continuité pour les semimartingales. Z.f.W. 35 (1976) 1–37

    Article  MathSciNet  MATH  Google Scholar 

  • Un théorème de représentation des martingales pour les ensembles régénératifs. Sem. Proba. Strasbourg X. Lecture Notes Springer 511 (1976) 24–39

    MathSciNet  MATH  Google Scholar 

  • JAGERS P. On the weak convergence of superpositions of point processes. Z.f.W. 22 (1972) 1–7

    Article  MathSciNet  MATH  Google Scholar 

  • On Palm probabilities. Z.f.W. 26 (1973) 17–32

    Article  MathSciNet  MATH  Google Scholar 

  • Aspects of random measures and point processes. Adv. Proba. 3, ed. Ney. M. Dekker (1974) 179–239

    MathSciNet  MATH  Google Scholar 

  • Convergence of general branching processes and functionals thereof J. Appl. Proba. 11 (1974) 471–8

    Article  MathSciNet  MATH  Google Scholar 

  • JAGERS P. et LINDVALL T. Thinning and rare events in point processes. Z.f.W. 28 (1974) 89–98 et 29 (1974) 272

    Article  MathSciNet  MATH  Google Scholar 

  • JIŘINA M. Branching process with measure-valued states. Trans. 3rd Prague Conf. (1964) 333–357

    Google Scholar 

  • KABANOV I. Représentation comme intégrales stochastiques des fonctionnelles d’un Wiener ou d’un Poisson. Teor. Veraj. Prim 18 (1973) 376–380

    MathSciNet  Google Scholar 

  • KABANOV I., LIPSER R. et SHIRYAEV A. Martingale methods in the theory of point processes. Proc. Steklov Inst. (1975) 269–354

    Google Scholar 

  • KAC M. et STEPIAN D. large excursions of Gaussian processes. Ann. Math. Stat. 30 (1959) 1215–1228

    Article  MathSciNet  MATH  Google Scholar 

  • KAILATH T. et SEGALL A. Radon-Nikodym derivatives with respect to measures induced by discontinuous independent increment processes. Ann. Proba 3 (1975) 449–464

    Article  MathSciNet  MATH  Google Scholar 

  • KALLENBERG O. Characterization and convergence of random measures and point processes. ZfW 27 (1973) 9–21

    MathSciNet  MATH  Google Scholar 

  • Canonical representations and convergence criteria for processes with interchangeable increments. ZfW 27 (1973) 23–36

    MathSciNet  MATH  Google Scholar 

  • Extremality of Poisson and sample processes. Stoch. Prob. Appli. 2 (1974) 73–83

    Article  MathSciNet  MATH  Google Scholar 

  • On symmetrically distributed random measures. Trans. AMS 202 (1975) 105–121

    Article  MathSciNet  MATH  Google Scholar 

  • Limits of compound and thinned point processes. J. Appl. Prob. 12 (1975) 269–278

    Article  MathSciNet  MATH  Google Scholar 

  • KENDALL D.G. Stochastic processes occuring in the theory of queues and their analysis by the method of the imbedded Markov chains. Ann. Math. Stat. 24 (1953) 338–354

    Article  MathSciNet  MATH  Google Scholar 

  • Foundations of a theory of random sets. Stochastic geometry. Harding et Kendall, ed. Wiley (1974) 322–376

    Google Scholar 

  • KERSTAN J. et MATTHES K. Verallgemernerungeines Satzes von Sliwnjak. Revue Romaine Math Pures et appliquées 9 (1964) 811–829

    MathSciNet  MATH  Google Scholar 

  • Ergodische unbegrenzt teilbare stationäre zufällige Punktfolgen. Trans. 4th Prague Conf (1967) 399–415

    Google Scholar 

  • KERSTAN J. MATTHES K. et MECKE J. Unbegrenzt teilbare Punktprozesse. Akademie Verlag, Berlin (1974)

    MATH  Google Scholar 

  • KIEFER J. et WOLFOWITZ J. On the theory of queues with many servers. Trans. AMS 78 (1955) 1–18

    Article  MathSciNet  MATH  Google Scholar 

  • On the characteristics of the general queuing process with applications to random walks. Ann. Math. Stat 27 (1956) 147–161

    Article  MathSciNet  MATH  Google Scholar 

  • KINGMAN J.F.C. On doubly stochastic Poisson processes. Proc Cambridge Phil Soc 60 (1964) 923–930

    Article  MathSciNet  MATH  Google Scholar 

  • The stochastic theory of regenerative events. ZfW 2 (1964) 180–224

    MathSciNet  MATH  Google Scholar 

  • Completely random measures. Pacific J. Math 21 (1967) 59–78

    Article  MathSciNet  MATH  Google Scholar 

  • Markov population processes. J. Appl. Proba. 6 (1969) 1–18

    Article  MathSciNet  MATH  Google Scholar 

  • Regenerative Phenomena. Wiley 1972

    Google Scholar 

  • KOSTEN L. Stochastic theory of service systems. Pergamon Press, Oxford (1973)

    MATH  Google Scholar 

  • KRENGEL U. Darstellungen von Strömungen I, II. Math. Annalen 176 (1968) 181–190

    Article  MathSciNet  MATH  Google Scholar 

  • KRICKEBERG K. The Cox processes. Symp. Math. Roma 9 (1972) 151–167

    MathSciNet  MATH  Google Scholar 

  • Theory of hyperplane processes. Conf. Stoch. point processes I.B.M. Wiley (1972) 514–521

    Google Scholar 

  • Moments of point processes. Lecture Notes in Mathematics, Springer 246 (1973) 70–101

    Article  MathSciNet  Google Scholar 

  • Invariance properties of the correlation measure of line processes. Stochastic geometry, ed. Kendall; Wiley (1974) 76–88

    Google Scholar 

  • KRYLOV N.V. et YUSKENI A.A. Markov random sets. Terr. Verojatn Prim. 9 (1964) 738–743

    MathSciNet  Google Scholar 

  • KUMMER G. et MATTHES K. Verallgemeinesung eines Satzes von Sliwnyak. Rev. Roumaine Math Pures Appl. 15 (1970) 845–870 et 1631–1642

    MathSciNet  MATH  Google Scholar 

  • KUNITA H. Asymptotic behavior of the non-linear filtering errors of Markov processes. J. Multiv. Anal. 1 (1971) 365–393

    Article  MathSciNet  MATH  Google Scholar 

  • Cours de 3ème cycle, Paris VI (1974)

    Google Scholar 

  • KUNITA H. et WATANABE S. Square integrable martingales. Nagoya J. Math 30 (1967) 209–245

    MathSciNet  MATH  Google Scholar 

  • KURTZ T.G. Limit theorem for sequences of jump Markov processes approximating ordinary differential processes. J. Appl. Proba. 8 (1971) 344–356

    Article  MathSciNet  MATH  Google Scholar 

  • Point processes and completely monotone set functions. ZfW 31 (1974) 57–67

    MathSciNet  MATH  Google Scholar 

  • LAWRANCE A.J. Selective interaction of a point process and a renewal process. J. Appl. Proba 7 (1970) 359–372, 7 (1970) 483–9, 8 (1971) 170–183, 8 (1971) 731–744

    Article  MathSciNet  MATH  Google Scholar 

  • Stationary series of univariate events. Stochastic point processes. P. Lewis, Ed. Wiley (1972) 199–256

    Google Scholar 

  • LAZARO J. de Sam et MEYER P.A. Méthodes des martingales et théorie des flots. ZfW 18 (1971) 116–140

    MATH  Google Scholar 

  • Questions de théorie des flots. Sém. Proba Strasbourg (1972–3)

    Google Scholar 

  • LEADBETTER M.R. On three basic results in the theory of stationary point processes. Proc. AMS 19 (1968) 115–7

    Article  MathSciNet  MATH  Google Scholar 

  • On basic results of point process theory. Proc. 6th Berkeley Symp 3 (1972) 449–462

    MathSciNet  MATH  Google Scholar 

  • Point processes generated by level crossings. Conf. Stoch. point processes I.B.M. Wiley (1972) 436–467

    Google Scholar 

  • LECAM L. An approximation theorem for the Poisson binomial distribution Pacific J. Math 10 (1960) 1181–1197

    MathSciNet  Google Scholar 

  • LEE P.M. Infinitely divisible stochastic processes. ZfW 7 (1967) 147–160

    MathSciNet  MATH  Google Scholar 

  • Some examples of infinitely divisible point processes. Studia Sc. Math Hung 3 (1968) 219–224

    MathSciNet  MATH  Google Scholar 

  • LEGALL Les systèmes avec ou sans attente et les processus stochastiques. Dunod 1962

    Google Scholar 

  • LEONOV V.P. Applications of the characteristic functional and semi-invariants to the ergodic theory of stationary processes. Dokl Akad Nauk SSSR (1960) 523–6

    Google Scholar 

  • LEWIS P.A.W. Asymptotic properties and equilibrium conditions for branching Poisson processes. J. Appl. Proba 6 (1969) 355–371

    Article  MathSciNet  MATH  Google Scholar 

  • Asymptotic properties of branching renewal processes

    Google Scholar 

  • LIND D.A. Locally compact measure preserving flows. Trans Amer Math Soc (1973)

    Google Scholar 

  • LITTLE D.V. A third note on recent research in general critical probability. Adv. Appl. Proba 6 (1974) 103–130

    Article  MathSciNet  MATH  Google Scholar 

  • MACCHI O. Etude d’un processus ponctuel par ses multicoīncidences. C.R. Acad. Sci. Paris 268 (1969) 1616, 271 (1970) 660

    MathSciNet  MATH  Google Scholar 

  • The coīncidence approach to stochastic point processes. Adv. Appl. Proba 7 (1975), 83–122

    Article  MathSciNet  MATH  Google Scholar 

  • MAISONNEUVE B. Temps local d’un fermé droit aléatoire: cas d’un ensemble régénératif. C.R. Acad. Sci. Paris A 270 (1970) 1526–8

    MathSciNet  MATH  Google Scholar 

  • Un résultat de renouvellement pour des processus de Markov généraux C.R. Acad. Sci. Paris A 272 (1971) 964–6

    MathSciNet  MATH  Google Scholar 

  • Ensembles régénératifs, temps locaux et subordinateurs. Sém. Proba. Strasbourg, Lecture Notes Mathematics Springer 191 (1971)

    Google Scholar 

  • MAISONNEUVE B. et MORANDO Ph. Temps locaux pour les ensembles régénératifs. CR. Acad. Sci. Paris A 269 (1969) 523–5

    MathSciNet  MATH  Google Scholar 

  • MARTINS-NETTO et WONG E. A martingale approach to queuing theory (1975)

    Google Scholar 

  • MARUYAMA Transformation of flows. J. Math. Soc. Japan 18 (1966) 303–330.

    Article  MathSciNet  MATH  Google Scholar 

  • MATHERON G. Ensembles aléatoires, ensembles semi-markoviens et polyèdres poissoniens. Adv. Appl. Proba. 4 (1972) 508–541

    Article  MathSciNet  MATH  Google Scholar 

  • Un théorème d’unicité pour les hyperplans poissoniens. J. Appl. Proba 11 (1974) 184–9

    Article  MathSciNet  MATH  Google Scholar 

  • Hyperplans poissoniens et compacts de Steiner. Adv. Appl. Proba 6 (1974) 563–579

    Article  MathSciNet  MATH  Google Scholar 

  • Random sets and integral geometry. Wiley 1975

    Google Scholar 

  • MATTHES K. Stationäre zufüllige Punktfolgen. Jahresbericht der DMV 66 (1963) 66–79

    MathSciNet  MATH  Google Scholar 

  • Zur theorie der Bedienungs prozesse. Trans. 3rd Prague Conf (1964) 513–518

    Google Scholar 

  • Eine charackterisierung der kontinuierlichen unbegrenzt teilbaren Verteinlungsgesetze zufälliger Punktfolgen. Revue Roumaine Math.Pures et appliquées 4 (1969) 1121–1127

    MathSciNet  MATH  Google Scholar 

  • Infinitely divisible point processes. Stochastic point processes, P. Lewis Ed. Wiley (1972) 384–404

    Google Scholar 

  • Mc FADDEN J.A. On the lengths of intervals in a stationary point processes. J.R. Stat. Soc. B 24 (1962) 364–382

    MathSciNet  Google Scholar 

  • Mc FADDEN J. et WEISSBLUM W. Higher order properties of a stationary point process. J.R. Stat. Soc. B 25 (1963) 413–431

    MathSciNet  MATH  Google Scholar 

  • MECKE J. Stationäre zufällige Masse auf lokalkompakten Abelschen Gruppen. ZfW 9 (1967) 36–58

    MathSciNet  MATH  Google Scholar 

  • Eine kharakteristischeEigenschaft der doppelt stochastischen Poissonschen Prozesse. ZfW 11 (1968) 74–81

    MathSciNet  MATH  Google Scholar 

  • Invariance Eigenschaften allgemeiner Palmscher Masse. Math. Nachrichten

    Google Scholar 

  • Dac Erlangsche Modell mit abhängigen Bedienungszeiten. Math. op. Forsch u Stat 3 (1972) 453–464

    Article  MathSciNet  MATH  Google Scholar 

  • Stationäre Verteilungen für das Erlangsche Modell. Math. Nachr

    Google Scholar 

  • A result on the output of stationary Erlang processes

    Google Scholar 

  • A characterization of mixed Poisson processes. J. Appl. Proba.

    Google Scholar 

  • MEYER P.A. Processus de Poisson ponctuels suivant Ito. Sém. Proba. Strasbourg V. Lecture Notes Springer 191 (1971)

    Google Scholar 

  • Ensembles aléatoires markoviens homogènes. Sém. Proba. Strasbourg 8, Lectures Notes Springer 381 (1974) 172–261

    MATH  Google Scholar 

  • Un cours sur les intégrales stochastiques. Sém. Proba. Strasbourg X, Lecture Notes Springer 511 (1975) 245–400

    Google Scholar 

  • Generation of σ-fields by step processes. Sem Strasbourg X. Lecture Notes Springer 511 (1976) 118–124

    MathSciNet  Google Scholar 

  • MILES R.E. Poisson flats in euclidean space. Adv. Appl. Proba. 1 (1969) 211–237 3 (1971) 1–43

    MathSciNet  MATH  Google Scholar 

  • A synopsis of Poisson flats in euclidean spaces. Izv. Akad Nauk Armianskoi SSR 3 (1970) 263–285

    MathSciNet  MATH  Google Scholar 

  • MILNE R.K. Simple proofs of some theorems on point processes. Ann. Math Stat 42 (1971) 368–372

    Article  MathSciNet  MATH  Google Scholar 

  • MILNE R.K. et WESTCOTT M. Further results for Gauss-Poisson processes. Adv. Appl. Proba. 4 (1972) 151–176

    Article  MathSciNet  MATH  Google Scholar 

  • MOGYÓRODI J. On the rarefaction of renewal processes. Studia Sci. Math. Hung 7 (1972) 285–305 et 8 (1973) 21–38, 193–209

    MathSciNet  MATH  Google Scholar 

  • MÖNCH G. Verallgeneinerung eines Satzes von A. Reyni. Studia Sci Math Hung 6 (1971) 81–90

    Google Scholar 

  • MORAN P.A.P. A non-markovian quasi-Poisson process. Studia Sci. Math Hung 2 (1967) 425–429

    MathSciNet  MATH  Google Scholar 

  • A second note on recent research in geometrical probability. Adv. Appl. Proba 1 (1969) 73–89

    Article  MathSciNet  MATH  Google Scholar 

  • MORI T. Ergodicity and identifiability for random translations of stationary point processes. J. Appl. Proba. 12 (1975) 734–743

    Article  MathSciNet  MATH  Google Scholar 

  • MOYAL J.E. The general theory of stochastic population processes. Acta Math 108 (1962) 1–31

    Article  MathSciNet  MATH  Google Scholar 

  • Multiplicative population processes. J. Appl. Proba. 1 (1964) 267–283

    Article  MathSciNet  MATH  Google Scholar 

  • Particle populations and number operators in quantum theory Adv. Appl. Proba. (1972) 39–80

    Google Scholar 

  • NEVEU J. Une généralisation des processus à accroissements positifs indépendants. Abh. Math. Sem. Hamburg 25 (1961) 36–61

    Article  MathSciNet  MATH  Google Scholar 

  • Bases mathématiques des Probabilités. Masson 1964 et 1970

    Google Scholar 

  • Sur la structure des processus ponctuels stationnaires. CR. Acad. Sci. Paris A 267 (1968) 561–4

    MathSciNet  MATH  Google Scholar 

  • Martingales à temps discret. Masson 1972

    Google Scholar 

  • Sur les measures de Palm de deux processus ponctuels stationnaires. ZfW 34 (1976) 189–203

    MathSciNet  MATH  Google Scholar 

  • NEWMAN D.S. A new family of point processes which are characterized by their second moment properties. J. Appl. Proba. 7 (1970) 338–358

    Article  MathSciNet  MATH  Google Scholar 

  • NEY P. Convergence of a random distribution function associated with a branching process. J. Math. Anal. Appl. 12 (1965) 316–327

    Article  MathSciNet  MATH  Google Scholar 

  • NGUYEN Xuan Xanh et ZESSIN H. Punktprozesse mit Wechselwirkung. ZfW 37 (1976) 91–126

    MathSciNet  MATH  Google Scholar 

  • OAKES D. Synchronous and asynchronous distributions for Poisson cluster processes. J. Roy Stat. Soc. B 37 (1975) 238–247

    MathSciNet  MATH  Google Scholar 

  • The markovian self exciting process. J. Appl. Proba. Appl. 12 (1975) 69–77

    Article  MathSciNet  MATH  Google Scholar 

  • Random overlopping intervals. A generalization of Erlang’s loss formula. Ann. Proba. 4 (1976) 940–6

    Article  MathSciNet  MATH  Google Scholar 

  • OREY S. Radon-Nikodym derivatives of probability measures: martingale methods. Dpt of Math. Educ., Tokyo Univ. Educ. (1974) 1–38

    Google Scholar 

  • PALM C. Intensitätschwankungen in Fernsprechverkehr. Ericsson Technics 44 (1943) 1–189

    MathSciNet  Google Scholar 

  • PAPANGELOU The Ambrose-Kakutani theorem and the Poisson process. Lecture Notes Springer 160 (1970)

    Google Scholar 

  • Integrability of expected increments of point processes and a related change of scale. Trans. AMS 165 (1972) 483–506

    Article  MathSciNet  MATH  Google Scholar 

  • Summary of some results on point and line processes. Stochastic point processes, etc ... I.B.M. Conf. Wiley (1972) 522–532

    Google Scholar 

  • Stochastic geometry. Trans. AMS 165 (1972) 483–506

    Article  MathSciNet  Google Scholar 

  • On the Palm probabilities of processes of points and processes of lines. Stochastic geometry, ed. Kendall. Wiley (1974) 114–147

    Google Scholar 

  • The conditional intensity of general point processes and an application to line processes. ZfW 28 (1974) 207–226

    MathSciNet  MATH  Google Scholar 

  • PARTHASARATHY K.R. Probability measures on metric spaces. Academic Press, New York 1967

    Book  MATH  Google Scholar 

  • POLLACZEK F. Problèmes stochastiques posés par le phénomène de formation d’une queue d’attente à un guichet et par des phénomènes apparentés Mém. Sc. Math Paris (1957)

    Google Scholar 

  • PORT S.C. Equilibrium systems of recurrent Markov processes. J. Math. Anal Appl. 12 (1965) 555–569

    Article  MathSciNet  MATH  Google Scholar 

  • Equilibrium processes Trans Amer Math Soc 124 (1966) 168–184

    Article  MathSciNet  Google Scholar 

  • Limit theorems involving capacities. J. Math. Mech 15 (1966) 805–832

    MathSciNet  MATH  Google Scholar 

  • PORT S.C. et STONE C.J. Infinite particle systems. Trans. Amer. Math. Soc. 178 (1973) 307–340

    Article  MathSciNet  MATH  Google Scholar 

  • PYKE R. Markov renenval processes. Ann. Math. Stat. 32 (1961) 1231–1259

    Article  MathSciNet  MATH  Google Scholar 

  • RÅDE L. Limit theorems for thinning of renewal point processes. J. Appl. Proba 9 (1972) 847–851

    Article  MathSciNet  MATH  Google Scholar 

  • RENYI A. Remarks on the Poisson process. Studia Sci Math Hung 2 (1967) 119–123

    MathSciNet  MATH  Google Scholar 

  • RENSHAW A. Interconnected population processes. J. Appl. Proba. 10 (1973) 1–14

    Article  MathSciNet  MATH  Google Scholar 

  • RIORDAN J. Stochastic service systems. Wiley (1962)

    Google Scholar 

  • RIPLEY R.D. Locally finite random sets; foundations for point process theory. Ann. Proba. 4 (1976) 983–994

    Article  MathSciNet  MATH  Google Scholar 

  • The foundations of stochastic geometry. Ann. Proba. 4 (1976) 995–998

    Article  MathSciNet  MATH  Google Scholar 

  • On stationary and superposition of point processes. Ann. Proba. 4 (1976) 999–1005

    Article  MathSciNet  MATH  Google Scholar 

  • ROOT D. A counterxample in renewal theory. Ann. Math. Stat. 42 (1971) 1763–6

    Article  MathSciNet  MATH  Google Scholar 

  • RUBEN H. et REED W.J. A more general form of a theorem of Crofton. J. Appl. Proba. 10 (1973) 479–482

    Article  MathSciNet  MATH  Google Scholar 

  • RUBIN I. Regular point processes and their detection. IEEE IT 18 (1972) 5

    Article  MathSciNet  MATH  Google Scholar 

  • Regular point processes and their information processing. IEEE IT 20 (1974) 617–624

    Article  MATH  Google Scholar 

  • RUDEMO M. Point processes generated by transition of Markov chains. Adv. Appl. Proba 5 (1973) 262–286

    Article  MathSciNet  MATH  Google Scholar 

  • Multivariate point processes generated by transitions of Markov chains. J. Appl. Proba (1973)

    Google Scholar 

  • Some non stationary point processes with stationary forward recurrence time distribution. J. Appl. Proba 12 (1975) 167–9

    Article  MathSciNet  MATH  Google Scholar 

  • RYLL NARDZEWSKI C Remarks on processes of calls. Proc 4th Berkeley Symp II (1961) 455–465

    MathSciNet  MATH  Google Scholar 

  • SAMUELS S.M. A characterization of the Poisson process. J. Appl. Proba 11 (1974) 72–85

    Article  MathSciNet  MATH  Google Scholar 

  • SERFLING R.J. Research in point processes, with applications to reliability and biometry. Proc. Conf. Florida. SIAM (1974) 109–127

    Google Scholar 

  • SERFOZO R.F. Conditional Poisson processes. J. Appl. Proba 9 (1972) 288–302

    Article  MathSciNet  MATH  Google Scholar 

  • Semi-stationary processes. ZfW 23 (1972) 125–132

    MathSciNet  MATH  Google Scholar 

  • Compositions, inverses and thinnings of random measures

    Google Scholar 

  • SERFOZO R. et STIDHAM S. Semi-stationary clearing processes

    Google Scholar 

  • SKOROHDD A. Studies in the theory of random processes. Trad. du russe. Addison-Wesley (1965)

    Google Scholar 

  • SLIVNYAK Some properties of stationary streams of homogeneous random events. Teor. Veraj. Prim. 7 (1962) 347–352

    MathSciNet  Google Scholar 

  • SNYDER D. Filtering and detection for doubly stochastic Poisson processes. IEEE Trans IT 18 (1972) 97–102

    MathSciNet  MATH  Google Scholar 

  • Smoothing for doubly stochastic Poisson processes. IEEE Trans IT 18 (1972) 558–562

    Article  MathSciNet  MATH  Google Scholar 

  • Information processing for observed jump processes. Info et Control 22 (1973)

    Google Scholar 

  • SRINIVASAN S.K. Stochastic point processes and their applications. Griffin’s Stat. Monographs and Courses 34 (1974)

    Google Scholar 

  • STONE C.J. On a theorem of Dobrusin. Ann Math Stat 39 (1968) 1391–1401

    Article  MATH  Google Scholar 

  • An supper bound for the renewal function. Ann Math Stat 43 (1972) 2050–2052

    Article  MATH  Google Scholar 

  • STÖRMER H. Zur Uberlagerung von Erneuerungs prozessen. ZfW 13 (1969) 9–24

    MATH  Google Scholar 

  • STRAUSS D.J. A model for clustering. Biometrika 62 (1975) 467–475

    Article  MathSciNet  MATH  Google Scholar 

  • SYSKI R. Introduction to Congestion theory in telephone systems. Oliver et Boyd, London (1962)

    Google Scholar 

  • SZASZ D. On the general branching process with continuous time-parameter. Studia Sci. Math Hung 2 (1967) 227–247

    MathSciNet  MATH  Google Scholar 

  • Once more on the Poisson process. Studia Sci. Math. Hung 5 (1970) 441–4

    MathSciNet  MATH  Google Scholar 

  • On the convergence of sums of point processes with integer marks Conf. on Stochastic point processes, etc. I.B.M. Wiley (1972) 607–615

    Google Scholar 

  • TAKACS L. Introduction to the theory of queues. Oxford Univ. Press (1962)

    Google Scholar 

  • Sojourn time problems. Ann. Proba. 2 (1974) 420–431

    Article  MathSciNet  MATH  Google Scholar 

  • TENHOOPEN M. and REUVER HA Selective interaction of two independent recurrent processes. J. Appl. Proba 2 (1965) 286–292

    Article  MathSciNet  MATH  Google Scholar 

  • Interaction between two independent recurrent time series. Info et Control 10 (1967) 149–158

    Article  MATH  Google Scholar 

  • THEDEEN T. A note on the Poisson tendency in traffic distribution. Annals Math Stat 35 (1964) 1823–4

    Article  MathSciNet  MATH  Google Scholar 

  • Convergence and invariance questions for point systems in R1 under random motion. Arkiv för Math 7 (1967) 211–239

    Article  MathSciNet  MATH  Google Scholar 

  • TOMKO J. On the rarefaction of multivariate point processes. European Meeting of Statisticians, Budapest (1972) 843–860

    Google Scholar 

  • TOTOKI H. Time changes of flows. Me Fac. Sci.Kyushu Univ. A 20 (1966) 27–55

    MathSciNet  MATH  Google Scholar 

  • TORTRAT A. Sur les mesures aléatoires dans les groupes non abéliens. Ann IHP 5 (1969) 31–47

    MathSciNet  MATH  Google Scholar 

  • VAN SCHUPPEN J. et WONG E. Translation of local martingales under a change of law. Ann. Proba. 2 (1974) 879–888

    Article  MATH  Google Scholar 

  • VARAYIA P. The martingale theory of jump processes. IEEE AC 20 (1975) 34–42

    Article  MathSciNet  Google Scholar 

  • VERE-JONES D. Stochastic models for earthquake occurence. JR Stat Soc B 32 (1970) 1–62

    MathSciNet  MATH  Google Scholar 

  • A renewal equation for point processes with Markov dependent intervals. Math. Nachr 68 (1975) 133–9

    Article  MathSciNet  MATH  Google Scholar 

  • VON WALDENFELS W. Charakteristische funktionale zufalliger Masse ZfW 10 (1968) 279–283

    MathSciNet  MATH  Google Scholar 

  • Taylor expansion of a Poisson measure. Sem Strasbourg. Lecture Notes Springer 381 (1974) 344–354

    Google Scholar 

  • WATANABE S. On discontinuous additive functionals and Levy measures of a Markov process. Japanese J. Math 34 (1964) 53–70

    MathSciNet  MATH  Google Scholar 

  • WEISS N.A. Infinite particle systems of recurrent random walks. J. Math Anal. Appl. 41 (1973) 563–574

    Article  MathSciNet  MATH  Google Scholar 

  • Limit theorems for infinite particle systems. ZfW

    Google Scholar 

  • WESTCOTT M. On existence and mixing results for cluster point processes. J.R. Stat. Soc. B 33 (1971) 290–300

    MathSciNet  MATH  Google Scholar 

  • The probability generating functional. J. Austr. Math. Soc. 13 (1972) 448–466

    Article  MathSciNet  MATH  Google Scholar 

  • Results in the asymptotic and equilibrum theory of Poisson cluster processes. J. Appl. Proba. 10 (1973) 807–823

    Article  MathSciNet  MATH  Google Scholar 

  • Some remarks on a property of the Poisson process. Sankhya A 35 (1973) 29–34

    MathSciNet  MATH  Google Scholar 

  • Simple proof of a result on thinned point process. Ann. Proba. 4 (1976) 89–90

    Article  MathSciNet  MATH  Google Scholar 

  • WHITT W. The continuity of queues. Adv. Appl. Proba. 6 (1974) 175–183

    Article  MathSciNet  MATH  Google Scholar 

  • Representation and convergence of point processes on the line. Ann. Proba. 2 (1974)

    Google Scholar 

  • WISMIEWSKI T.K.M. Bivariate stationary point processes. Adv. Appl. Proba. 4 (1972) 296–317

    Article  Google Scholar 

  • WONG E. Recent progresses in stochastic processes; a survey. IEEE Trans. IT 19 (1973) 262–275

    Article  MATH  Google Scholar 

  • WOLFF R.W. et WRIGHTSON C.W. An extension of Erlang’s loss formula. J. Appl. Proba. 13 (1976) 628–632

    Article  MathSciNet  MATH  Google Scholar 

  • YASHIN Filtering of jump processes. Artomatika i Telemektanica 5 (1970)

    Google Scholar 

  • YLVISAKER N.D. The expected number of zeros of a stationary Gaussian process. Ann. Math. Stat. 36 (1965) 1043–6

    Article  MathSciNet  MATH  Google Scholar 

  • YOR M. Sur les intégrales stochastiques optionnelles et une suite remarquable de formules exponentielles. Sém. Proba. Strasbourg, Lecture Notes Springer (1975)

    Google Scholar 

  • Représentation des martingales de carré intégrable relative aux processus de Wiener et de Poisson à n paramètres. C.R. Acad. Sci. Paris 281 (1975) 111–113

    MATH  Google Scholar 

  • YOEURP CH. Décomposition de martingales locales et formules exponentielles. Sém. Proba. Strasbourg, Lecture Notes Springer.

    Google Scholar 

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Neveu, J. (1977). Processus ponctuels. In: Hennequin, P.L. (eds) Ecole d’Eté de Probabilités de Saint-Flour VI-1976. Lecture Notes in Mathematics, vol 598. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0097494

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