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Stationary excursions

Part of the Lecture Notes in Mathematics book series (SEMPROBAB,volume 1247)

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References

  • ATKINSON, B. W. and MITRO, J. B. (1983). Applications of Revuz and Palm type measures for additive functionals in weak duality. Seminar on stochastic processes 1982. Birkhäuser, Boston.

    Google Scholar 

  • AZEMA, J., DUFLO, M. and REVUZ, D. (1967). Mesure invariante sur les classes récurrentes des processus de Markov. Z. Wahrscheinlichkeitstheorie 8, 157–181.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • AZEMA, J., DUFLO, M. and REVUZ, D. (1969). Propriétés relatives des processus de Markov récurrents. Z. Wahrscheinlichkeitstheorie 13, 286–314.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • BIANE, P. (1986). Relations entre pont et excursion du mouvement brownien réel. Ann. Inst. Henri. Poincaré, Prob. et Stat, 22, 1–7.

    MathSciNet  MATH  Google Scholar 

  • BISMUT, J. M. (1985). Last exit decomposition and regularity at the boundary of transition probabilities. Z. Wahrscheinlichkeitstheorie 69, 65–98.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • BLUMENTHAL, R. M. and GETOOR, R. K. (1968). Markov processes and potential theory. Academic Press.

    Google Scholar 

  • BURDZY, K. (1986). Brownian excursions from hyperplanes and smooth surfaces. T.A.M.S. 295, 35–57.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • BURDZY, K., PITMAN, J. W. and YOR, M. Asymptotic laws for crossings and excursions. Paper in preparation.

    Google Scholar 

  • DE SAM LAZARO, J. and MEYER, P. A. (1975). Hélices croissantes et mesures de Palm. Séminaire de Prob. IX pp. 38–51. Lecture Notes in Math. 465.

    Google Scholar 

  • DYNKIN, E. B. (1985). An application of flows to time shift and time reversal in stochastic processes. T.A.M.S. 287, 613–619.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • FITZSIMMONS, P. J. & MAISONNEUVE, B. (1986). Excessive measures and Markov processes with random birth and death. Probability Theory and Related Fields 72, 319–336.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • FRANKEN, P., KONIG, D., ARNDT, V., SCHMIDT, V. (1981). Queues and point processes. Wiley and sons, New York.

    MATH  Google Scholar 

  • GEMAN, D. & HOROWITZ, J. (1973). Remarks on Palm measures. Ann. Inst. Henri Poincaré Sec B, IX 213–232.

    MathSciNet  MATH  Google Scholar 

  • GETOOR, R. K. (1979). Excursions of a Markov process. Ann. Probab. 7, 244–266.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • GETOOR, R. K. (1985). Some remarks on measures associated with homogeneous random measures. To appear. Sem. Stoch. Proc. 1985. Birkhäuser, Boston.

    Google Scholar 

  • GETOOR, R. K. (1985). Measures that are translation invariant in one coordinate. Preprint.

    Google Scholar 

  • GETOOR, R. K. & SHARPE, M. J. (1981). Two results on dual excursions. Seminar on stochastic processes 1981. Boston. p. 31–52. Birkhäuser.

    Google Scholar 

  • GETOOR, R. K. & SHARPE, M. J. (1982). Excursions of Dual processes. Adv. in Math. 45, 259–309

    CrossRef  MathSciNet  MATH  Google Scholar 

  • GETOOR, R. K. & SHARPE, M. J. (1984). Naturality, standardness, and weak duality for Markov processes. Z. Wahrscheinlichkeitstheorie, 67, 1–62.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • GETOOR, R. K. & STEFFENS, J. (1985). Capacity theory without duality. Preprint

    Google Scholar 

  • GREENWOOD, P. and PITMAN, J. W. (1980a). Construction of local time and Poisson point processes from nested arrays. J. London Math. Soc. (2) 22, 182–192.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • GREENWOOD, P. and PITMAN, J. W. (1980b). Fluctuation identities for Lévy processes and splitting at the maximum. Adv. Appl. Prob. 12, 893–902.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • HSU, P. (1986). On excursions of reflecting Brownian motion. To appear in T.A.M.S.

    Google Scholar 

  • ITÔ, K. (1970). Poisson point processes attached to Markov processes. Proc. Sixth Berkeley Symp. Math. Statist. Prob. pp. 225–239. Univ. of California Press, Berkeley.

    Google Scholar 

  • JACOD, J. (1979). Calcul Stochastique et Problèmes de Martingales. Lecture Notes in Math. 714, Springer-Verlag, Berlin.

    MATH  Google Scholar 

  • KASPI, H. (1983). Excursions of Markov processes: An approach via Markov additive processes. Z. Wahrscheinlichkeitstheorie verw. Gebiete. 64, 251–268.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • KASPI, H. (1984). On invariant measures and dual excursions of Markov processes. Z. Wahrscheinlichkeitstheorie 66, 185–204.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • KERSTAN, J., MATTHES, K. and MECKE, J. (1974). Infinitely divisible point processes. Wiley and sons. New York.

    MATH  Google Scholar 

  • KUZNETSOV, S. E. (1974). Construction of Markov processes with random times of birth and death. Th. Prob. Appl., 18, 571–574.

    CrossRef  MATH  Google Scholar 

  • MAISONNEUVE, B. (1971). Ensembles régénératifs, temps locaux et subordinateurs. Sém. de Prob. V. Lecture Notes in Math 191.

    Google Scholar 

  • MAISONNEUVE, B. (1975). Exit systems. Ann. Prob. 3, 399–411.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • MAISONNEUVE, B. (1983). Ensembles régénératifs de la droite. Z. Wahrscheinlichkeitstheorie 63, 501–510.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • MATTHES, K. (1963/4). Stationäre zufällige Punktfolgen. Jahresbericht d. Deutsch. Math. Verein, 66, 66–79.

    MathSciNet  MATH  Google Scholar 

  • MCFADDEN, J. A. (1962). On the lengths of intervals in a stationary point process J. Roy. Stat. Soc. Ser. B, 24, 364–382.

    MathSciNet  MATH  Google Scholar 

  • MECKE, J. (1967). Stationäre zufällige Masse auf lokal kompakten Abelschen Gruppen. Z. Wahrscheinlichkeitstheorie 9, 36–58.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • MITRO, J. B. (1979). Dual Markov processes: Construction of a useful auxilliary process. Z. Wahrscheinlichkeitstheorie 47, 139–156.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • MITRO, J. B. (1984). Exit systems for dual Markov processes. Z. Wahrscheinlichkeitstheorie 66, 259–267.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • NEVEU, J. (1968). Sur la structure des processes ponctuels stationaires. C. R. Acad. Sci, t 267, A p. 561.

    MathSciNet  MATH  Google Scholar 

  • NEVEU, J. (1976). Sur les mesures de Palm de deux processus ponctuels stationnaires. Z. Wahrscheinlichkeitstheorie verw. Geb. 34, 199–203.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • NEVEU, J. (1977). Ecole d'Eté de Probabilités de Saint-Flour VI-1976. 250–446. Lecture Notes in Math. 598. Springer.

    Google Scholar 

  • PITMAN, J. W. (1981). Lévy systems and path decompositions. Seminar on stochastic processes 1981. Birkhäuser, Boston.

    Google Scholar 

  • SHARPE, M. J. (1972). Discontinuous additive functionals of dual Markov processes. Z. Wahrscheinlichkeitstheorie 21, 81–95.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • TAKSAR, M. I. (1980). Regenerative sets on the real line. Seminaire de probabilités XIV, Springer Lecture notes in math. 784.

    Google Scholar 

  • TAKSAR, M. I. (1981). Subprocesses of a stationary Markov process. Z. Wahrscheinlichkeitstheorie 55, 275–299.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • TAKSAR, M. I. (1983). Enhancing of semigroups. Z. Wahrscheinlichkeitstheorie 63, 445–462.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • TAKSAR, M. I. (1986). Infinite excessive and invariant measures. Preprint.

    Google Scholar 

  • TOTOKI, H. (1966). Time changes of flows. Mem. Fac. Sci. Kyūshū Univ. Ser. A. t, 20, p. 27–55.

    MathSciNet  MATH  Google Scholar 

  • VERVAAT, W. (1979). A relation between Brownian bridge and Brownian excursion. Ann. Prob. 7, 143–149.

    CrossRef  MathSciNet  MATH  Google Scholar 

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Pitman, J. (1987). Stationary excursions. In: Azéma, J., Yor, M., Meyer, P.A. (eds) Séminaire de Probabilités XXI. Lecture Notes in Mathematics, vol 1247. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0077643

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  • DOI: https://doi.org/10.1007/BFb0077643

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