Abstract
The survey is devoted to works appearing in the last 3–5 years and pertaining mainly to local properties of the trajectories of Gaussian processes, the behavior of trajectories in the uniform metric, and properties of level sets. Some new results are also presented.
Similar content being viewed by others
Literature cited
Yu. K. Belyaev, “On the unboundedness of sample functions of Gaussian processes,” Teor. Veroyatn. Primen.,3, No. 3, 351–354 (1958).
Yu. K. Belyaev, “On the number of level crossings by a Gaussian stochastic process. II,” Teor. Veroyatn. Primen.,12, No. 3, 444–457 (1967).
Yu. K. Belyaev and V. I. Piterbarg, “Asymptotics of the mean number of A-points of crossings of a Gaussian field beyond a high level,” Dokl. Akad. Nauk SSSR,203, No. 1, 9–12 (1972).
Yu. K. Belyaev and A. Kh. Simonyan, “Asymptotic properties of the deviations of the realization of a Gaussian process from an approximating broken line with reduction of the step size of quantization,” in: Sluch, Protsessy i Polya [in Russian], Moscow (1979), pp. 9–21.
S. Berman, “Sojourn times and extrema of Gaussian processes,” in: Stochastic Processes [in Russian], Moscow (1978), pp. 164–203.
M. G. Bilyk, “Statistical properties of level crossings of a periodically nonstationary process and a periodically inhomogeneous field,” Otbor i Peredacha Inform., Resp. Mezhved., Sb., No. 52, 3–8 (1977).
M. G. Bilyk, “Some properties of the extrema of a nonstationary Gaussian process,” Otbor i Peredacha Inf. (Kiev), No. 56, 13–17 (1979).
V. V. Buldygin, Convergence of Random Elements in Topological Spaces [in Russian], Naukova Dumka, Kiev (1980).
N. N. Vakhaniya, “On the correspondence between the concepts of a Gaussian measure and a Gaussian process,” Mat. Zametki,26, No. 2, 293–297 (1979).
A. D. Venttsel' and M. I. Freidlin, Fluctuations in Dynamical Systems Under the Action of Small Random Perturbations [in Russian], Nauka, Moscow (1979).
V. A. Volkonskii and Yu. A, Rozanov, “Some limit theorems for random functions. I,” Teor. Veroyatn. Primen.,4, No. 2, 186–207 (1959).
N. A. Geodakov, “The local Markov property of stationary Gaussian processes,” Teor. Veroyatn. Primen.,24, No. 4, 854–858 (1979).
N. A. Geodakov, “The local Markov property of processes of class (2k+1),” Upr., Nadezhnost' i Navigatsiya (Saransk), No. 5, 165–168 (1979).
H. H. Kuo, Gaussian Measures in Banach Spaces, Springer-Verlag (1975),
V. V. Gorodetskii, “The invariance principle for functions of stationary, connected Gaussian variables,” Probl. Teor. Veroyatn. Raspredelenii, VI, Leningrad (1980), pp. 32–44.
Yu. A. Davydov, “Local times for multiparameter stochastic processes,” Teor. Veroyatn. Primen.,23, No. 3, 594–605 (1978).
R. M. Dudley, “Sample functions of a Gaussian process,” in: Sluchain. Protsessy, Moscow (1978), pp. 7–62.
V. A. Dmitrovskii, “Estimate s of the distribution of the maximum of a Gaussian Field,” in: Sluch. Protsessy i Polya [in Russian], Moscow (1979), pp. 22–31.
V. A. Dmitrovskii, “Boundedness conditions and estimates of the distribution of the maximum of random fields on arbitrary sets,” Dokl. Akad. Nauk SSSR,253, No. 2, 271–274 (1980).
N. M. Zinchenko, “On the p-variation of Gaussian random fields,” Teor. Veroyatn. Mat. Stat., Resp. Mezhved. Nauch. Sb., No. 19, 72–76 (1978).
I. A. Ibragimov, “On the probability of a Gaussian vector with values in a Hilbert space entering a sphere of small radius,” Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst. Akad. Nauk SSSR,85, 75–93 (1979).
I. A. Ibragimov and Yu. A. Rozanov, Gaussian Stochastic Processes [in Russian], Nauka, Moscow (1970).
V. D. Konakov, “An estimate of the rate of convergence of the distribution of the maximum modulus of a nondifferentiable Gaussian process,” in: Mnogomern. Stat. Analiz, Mat. Obespech., Moscow (1975), pp. 101–115.
V. D. Konakov, “Asymptotic expansions for the probability of large deviations of Gaussian stationary sequences,” in: Mnogomern. Stat. Analiz, Mat. Obespech., Moscow (1979), pp. 116–121.
V. D. Konakov and V. I. Piterbarg, “Large deviations of Gaussian processes and empirical densities,” Teor. Veroyatn. Primen.,3, 658–659 (1979).
G. Cramer and M. R. Lidbetter, Stationary Stochastic Processes [Russiantranslation], Mir, Moscow (1969).
M. A. Lifshits, “Local times for Gaussian processes,” Teor. Veroyatn. Primen.,23, No. 4, 867–868 (1978).
M. A. Lifshits, “Transport of a measure by trajectories of a stationary Gaussian process,” Teor. Veroyatn. Primen.,24, No. 2, 432 (1979).
M. A. Lifshits, “On the representation of Levy fields by indicators,” Teor. Veroyatn. Primen.,24, No. 3, 624–628 (1979).
M. A. Lifshits, “Local times for functions and Gaussian processes,” Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst. Akad. Nauk SSSR,85, 104–112 (1979).
T. L. Malevich, “On the probability of finding a stationary Gaussian process above the zero level,” in: Veroyatnostn. Protessy i Mat. Stat., Tashkent (1978), pp. 79–87.
T. L. Malevich, “On conditions for the finiteness of the moments of the number of zeros of stationary Gaussian processes,” Teor. Veroyatn. Primen.,24, No. 4, 741–753 (1979).
T. L. Malevich and L. N. Volodina, “Inequalities for the moments of the number of zeros of a stationary Gaussian process. I,” Izv. Akad. Nauk Uzb. SSR, Ser. Fiz.-Mat., No. 5, 30–36 (1978).
T. L. Malevich and L. N. Volodina, “Inequalities for the moments of the number of zeros of a stationary Gaussian process. II,” Izv. Akad. Nauk Uzb. SSR, Ser. Fiz.-Mat. Nauk, No. 2, 29–33 (1979).
T. L. Malevich and N. Toshov, “On the boundaries of the maximum of a homogeneous Gaussian field,” Teor. Veroyatn. Mat. Stat. (Kiev), No. 20, 76–90 (1979).
T. L. Malevich and N. Toshov, “On the asymptotic behavior of the maximum of Gaussian processes and fields,” Izv. Akad. Nauk Uzb. SSR, Ser. Fiz.-Mat. Nauk, No. 6, 8–10 (1977).
T. L. Malevich and N. Toshov, “On the maximum of a nonstationary Gaussian process,” in: Veroyatnostn. Protsessy i Mat. Stat., Tashkent (1978), pp. 88–95.
V. A. Malyshev, “Cluster expansions and lattice models of statistical physics and quantum field theory,” Usp. Mat. Nauk,35, No. 2, 3–53 (1980).
G. V. Martynov, “Computation of a function of the normal distribution,” Itogi Nauki i Tekh. VINITI. Teoriya Veroyatnostei. Mat. Stat. Teor. Kibernet.,17, 57–84 (1979).
I. K. Matsak, “Regularity of sample functions of a stochastic process,” Ukr. Mat. Zh.,30, No. 2, 241–247 (1978).
I. K. Matsak, “Asymptotic properties of Gaussian processes,” Ukr. Mat. Zh.,32, No. 3, 332–339 (1980).
R. N. Miroshin, “Conditions for the finiteness of the moments of the number of zeros for stationary Gaussian processes,” Teor. Veroyatn. Primen.,22, No. 3, 631–641 (1977).
R. N. Miroshin, “Conditions of local regularity for differentiable Gaussian processes,” Teor. Veroyatn. Primen.,22, No. 4, 851–856 (1977).
R. N. Miroshin, “A sufficient condition for local regularity of first order for stationary Gaussian processes,” Vestn. Leningr. Gos. Univ., No. 7, 98–106 (1978).
R. N. Miroshin, “Markov and recurrent stationary Gaussian processes of second order,” Teor. Veroyatn. Primen.,24, No. 4, 847–853 (1979).
R. N. Miroshin, “On conditions of local regularity and the finiteness of moments of the number of zeros for a differentiable stationary Gaussian process,” Vestn. Leningr. Gos. Univ., No. 7, 83–92 (1980).
S. A. Molchanov and A. K. Stepanov, “Bursts of a Gaussian field over a high level,” Dokl. Akad. Nauk SSSR,249, No. 2, 294–297 (1979).
S. A. Molchanov and A. K. Stepanov, “The estimate of V. A. Malyshev for the moments of Wick polynomials and some of its applications,” in: Sluch. Protessy i Polya [in Russian], Moscow (1979), pp. 39–48.
G. A. Nesenenko and Yu. N. Tyurin, “Asymptotics of the Kolmogorov statistics for a nonparameteric family,” Dokl. Akad. Nauk SSSR,239, No. 6, 1292–1294 (1978).
V. P. Nosko, “On the definition of the number of crossings of a random field beyond a fixed level,” Teor. Veroyatn. Primen.,24, No. 3, 592–596(1979).
E. I. Ostrovskii, “Monotonicity of Gaussian operators,” in: Sluch. Protessy i Polya [in Russian], Moscow (1979), pp. 54–61.
V. I. Piterbarg, “Some directions in the investigation of properties of the trajectories of Gaussian random functions, appendix-survey,” Sluchain. Protsessy [in Russian], Moscow (1978), pp. 258–280.
V. I. Piterbarg, “Asymptotic expansions for the probabilities of large deviations of Gaussian processes,” Dokl. Akad. Nauk SSSR,242, No. 6, 1248–1251 (1978).
V. I. Piterbarg, “Refinement of the limit theorem for the maximum of a stationary Gaussian process,” Sluch. Protsessy i Polya [in Russian], Moscow (1979), pp. 62–70.
V. I. Piterbarg, “Asymptotic expansions in the Poisson limit theorem for large deviations of a stationary Gaussian sequence,” Mat. Zametki,29, No. 1, 131–144 (1980).
V. I. Piterbarg, “The Poisson limit theorem for large deviations of a Gaussian sequence,” Dokl. Akad. Nauk SSSR,257, No. 1, 48–50 (1981).
V. I. Piterbarg and V. P. Prisyazhnyuk, “Asymptotics of the probability of large deviation for a nonstationary Gaussian process,” Teor. Veroyatn. Mat. Stat., Resp. Mezhved. Nauch. Sb., No. 18, 121–134 (1978).
A. Plikunas, “Estimates of semiinvariants and large deviations for certain nonlinear transformations of a stationary Gaussian process,” Lit. Mat. Sb.,20, No. 2, 119–128 (1980).
Yu. A. Rozanov, Markov Random Fields [in Russian], Nauka, Moscow (1981).
A. A. Rusakov, “Asymptotic estimates of the probability of deviation of integrals of weakly correlated Gaussian processes,” Sluch. Protsessy i Polya [in Russian], Moscow (1979), pp. 78–83.
O. V. Seleznev, “Approximation of periodic Gaussian processes by trigonometric polynomials,” Dokl. Akad. Nauk SSSR,250, No. 1, 35–38 (1980).
O. V. Seleznev, “On the approximation of continuous periodic Gaussian processes by random trigonometric polynomials,” Sluch. Protsessy i Polya [in Russian], Moscow (1979), pp. 84–94.
A. Kh. Simonyan, “On the probability of deviation of a Gaussian random process from an approximating random curve,” Dokl. Akad. Nauk Arm. SSR,66, No. 2, 84–90 (1978).
V. F. Sinyavskii, “A lower bound for the modulus of continuity of homogeneous random Gaussian fields,” in: Veroyatnostnye Raspredeleniya v Beskonechnomern. Prostranstvakh, Kiev (1978), pp. 135–143.
V. F. Sinyavskii, “An upper bound for the modulus of continuity of sample functions of homogeneous Gaussian random fields,” Teor. Veroyatn. Mat. Stat., No. 21, 148–152 (1979).
V. F. Sinyavskii, “On the modulus of continuity of sample functions of homogeneous Gaussian random fields,” Dokl. Akad. Nauk Ukr. SSR, A, No. 2, 22–24 (1980).
V. F. Sinyavskii, “Conditions for the discontinuity of sample functions of homogeneous Gaussian random fields,” Teor. Veroyatn. Mat. Stat. (Kiev), No. 22, 131–135 (1980).
Yu. K. Belyaev (ed.), Stochastic Processes. Sample Functions and Intersections [Russian translation] (a collection of papers), Mir, Moscow (1978).
V. N. Sudakov, “Gaussian random processes and measures of solid angles in Hilbert space,” Dokl. Akad. Nauk SSSR,197, No. 1, 43–45 (1971).
V. N. Sudakov, “Geometric problems of the theory of infinite-dimensional probability distributions,” Tr. Mat. Inst. Akad. Nauk SSSR,141 (1976).
G. N. Sytaya, “On small spheres of Gaussian measures,” in: Probability Distributions in Infinite-Dimensional Spaces [in Russian], Kiev (1978), pp. 154–171.
N. Toshov, “On asymptotic normality of surpassing Zn-characteristics of a stationary Gaussian process,” Izv. Akad. Nauk Uzb. SSR, Ser. Fiz.-Mat. Nauk, No. 2, 27–31 (1978).
X. Fernique, “Regularity of the trajectories of Gaussian random functions,” Sluchain. Protsessy [in Russian], Moscow (1978), pp. 63–122.
I. A. Khalidov, “Gaussian recurrent random processes,” Redkol. Zh. Vestn. Leningr. Gos. Univ., Mat., Mekh., Astron., Leningrad (1979).
U. Tsele, “Asymptotic behavior of the flow of rare events of a Gaussian field,” Dokl. Akad. Nauk SSSR,249, No. 3, 562–565 (1979).
U. Tsele, “The Poisson limit theorem for rare events of a Gaussian sequence,” Teor. Veroyatn. Primen.,25, No. 1, 92–104 (1980).
B. S. Tsirel'son, “The density of the distribution of the maximum of a Gaussian process,” Teor. Veroyatn. Primen.,20, No. 4, 865–873 (1975).
M. I. Yadrenko, Spectral Theory of Random Fields [in Russian], Vishcha Shkola, Kiev (1980).
R. J. Adler, “Distribution results for the occupation measures of continuous Gaussian fields,” Stochast. Process. Appl.,7, No. 3, 299–310 (1978).
R. J. Adler, “On the envelope of a Gaussian random field,” J. Appl. Probab.,15, No. 3, 502–513 (1978).
S. M. Berman, “A law of large numbers for the maximum in a stationary Gaussian sequence,” Ann. Math. Stat.,33, No. 1, 93–97 (1962).
S. M. Berman, “Limit theorems for the maximum term in stationary sequences,” Ann. Math. Stat.,35, No. 2, 502–516 (1964).
S. M. Berman, “Asymptotic independence of the numbers of high and low level crossings of stationary Gaussian processes,” Ann. Math. Stat.,42, No. 3, 927–945 (1971).
S. M. Berman, “A new kind of tightness of probability measures and its applications to integral functionals of stochastic processes,” Z. Wahr. Verw. Geb.,42, No. 2, 155–165 (1978).
S. M. Berman, “Gaussian processes with biconvex covariances,” J. Multivar. Anal.,8, No. 1, 30–44 (1978).
S. M. Berman, “High level sojourns for strongly dependent Gaussian processes,” Z. Wahr. Verw. Geb.,50, No. 2, 223–236 (1979).
S. M. Berman, “A compound Poisson limit for stationary sums and sojourns of Gaussian processes,” Ann. Probab.,8, No. 3, 511–538 (1980).
S. M. Berman, “Isotropic Gaussian processes on the Hilbert sphere,” Ann. Probab.,8, No. 6, 1093–1106 (1980).
J. Cuzick, “A lower bound for the prediction error of stationary Gaussian processes,” Indiana Univ. Math. J.,26, No. 3, 577–584 (1977).
J. Cuzick, “Some local properties of Gaussian vector fields,” Ann. Probab.,6, No. 6, 984–994 (1978).
J. Cuzick, “The Hausdorff dimension of the level sets of a Gaussian vector field,” Z. Wahr. Verw. Geb.,51, No. 3, 287–290 (1980).
J. Cuzick and G. Lingren, “Frequency estimation from crossings of an unknown level,” Biometrika,67, No. 1, 65–72 (1980).
L. P. Davies, “The exact Hausdorff measure of the zero set of certain stationary Gaussian processes,” Ann. Probab.,5, No. 5, 740–755 (1977).
J. Delporte, “Fonctions aléatoires presque surement continues sur un intervalle fermé,” Ann. Inst. H. Poincaré,B1, No. 2, 8–215 (1964).
J. De Mare, “The behavior of a nondifferentiable stationary Gaussian process after a level crossing,” Stochast. Processes Appl.,6, No. 1, 77–86 (1977).
J. Diebolt, “Sur la loi du maximum de certains processus gaussiens sur le tore,” C. R. Acad. Sci.,AB290, No. 19, A913-A915 (1980).
R. L. Dobrushin and P. Major, “Noncentral limit theorems for nonlinear functionals of Gaussian fields,” Z. Wahr. Verw. Geb.,50, No. 1, 27–52 (1979).
R. M. Dudley, “The sizes of compact subsets of Hilbert space and continuity of Gaussian processes,” J. Funct. Anal.,1, No. 3, 290–330 (1967).
R. M. Dudley, “Lower layers in R2 and convex sets in R3 are not GB classes,” Lect. Notes Math.,709, 97–102 (1979).
X. Fernique, “Evaluations des processus gaussiens,” Symp, Math. Iust. Naz. Alta Mat., Vol. 21, London-New York (1977), pp. 91–100.
X. Fernique, “Characterisation de processus a trajectoires majorées ou continues,” Lect. Notes Math.,649, 691–706 (1978).
X. Fernique, “Random functions and Orlicz's method of regularity of paths and limit properties,” Lect. Notes Math.,656, 31–36 (1978).
W, Fieger, “Die Anzahl der Kreuzungspunkte einer Funktion mit einem Gausschen Prozess,” Trans. 7th Prague Conf. Inform. Theory, Statist. Decision Funct., Random Processes and 1974 Eur. Meet. Statist., Prague, 1974, Vol. A, Prague (1977), pp. 135–146.
H. V. Hebbar, “Almost sure limit points of maxima of stationary Gaussian sequences,” Ann. Probab.,8, No. 2, 393–399 (1980).
J. Hoffmann-Jorgensen, L. A. Shepp, and R. M. Dudley, “On the lower tail of Gaussian seminorms,” Prepr. Ser. Mat. Inst. Aarhus Univ., 1976–1977, No. 40 (1977).
J. Hoffmann-Jorgensen, L. A. Shepp, and R. M. Dudley, “On the lower tail of Gaussian seminorms,” Ann. Probab.,7, No. 2, 319–342 (1979).
J. Husler, “On limit distributions of first crossing point of Gaussian sequences,” Stochast. Processes and Appl.,6, No. 1, 65–75 (1977).
J. Husler, “Almost sure limiting behavior of first crossing points of Gaussian sequences,” Stochast. Processes and Appl.,8, No. 3, 315–321 (1979).
Chii-Ruey Hwang, “Gaussian measure of large balls in a Hilbert space,” Proc. Am. Math. Soc.,78, No. 1, 107–110 (1980).
R. Jaimez and Takayuki Kawada, “A comparison theorem of Marcus-Shepp in the uniform continuity of Gaussian processes,” Trab. Estadist. Invest. Oper.,30, No. 1, 83–88 (1979).
N. C. Jain and M. B. Marcus, “Continuity of subgaussian processes,” Probab. Banach Spaces, New York-Basel (1978), pp. 81–196.
O. Kallenberg, “Characterization and convergence of random measures and point processes,” Z. Wahr. Verw. Geb.,27, No. 1, 9–21 (1973).
Takayuki Kawada, “Maximum in the Levy-Baxter theorem for Gaussian random fields,” Ann. Probab.,7, No. 1, 173–178 (1979).
N. Kono, “Holder conditions for the local times of certain Gaussian processes with stationary increments,” Proc. Jpn. Acad., A,53, No. 3, 84–87 (1977).
N. Kono, “Double points of a Gaussian sample path,” Z. Wahr. Verw. Geb.,45, No. 2, 175–180 (1978).
G. Lindgren, “Functional limits of empirical distributions in crossing theory,” Stochast. Processes Appl.,5, No. 2, 143–149 (1977).
G. Lindgren, “Prediction of level crossings for normal processes containing deterministic components,” Adv. Appl. Probab.,11, No. 1, 93–117 (1979).
G. Lindgren, “Point processes of exist by bivariate Gaussian processes and extremal theory for the χ2-process and its concomitants,” J. Multivar. Anal.,10, No. 2, 181–206 (1980).
G. Lindgren, “Model processes in nonlinear prediction with application to detection and alarm,” Ann. Probab.,8, No. 4, 775–792 (1980).
G. Lindgren, “Extreme values and crossing for the χ2-process and other functions of multidimensional Gaussian processes with reliability applications,” Adv. Appl. Probab.,12, No. 3, 746–774 (1980).
M. B. Marcus, “Level crossings of a stochastic process with absolutely continuous sample paths,” Ann. Prob.,5, No. 1, 52–71 (1977).
M. B. Marcus, L. A. Shepp, “Continuity of Gaussian processes,” Trans. Am. Math. Soc.,151, No. 2, 377–391 (1970).
W. P. McCormick, “Weak convergence for the maxima of stationary Gaussian processes using random normalization,” Ann. Probab.,8, No. 3, 483–497 (1980).
W. P. McCormick, “An extension to a strong law result of Mittal and Ylvisaker for the maxima of stationary Gaussian processes,” Ann. Probab.,8, No. 3, 498–510 (1980).
Y. Mittal, “Maxima of partial samples in Gaussian sequences,” Ann. Probab.,6, No. 3, 421–432 (1978).
Y. Mittal, “A new mixing condition for stationary Gaussian processes,” Ann. Probab.,7, No. 4, 724–730 (1979).
Y. Mittal and D. Ylvisaker, “Limit distributions for the maxima of stationary Gaussian processes,” Stochast. Processes Appl.,3, No. 1, 1–18 (1975).
Y. Mittal and D. Ylvisaker, “Strong laws for the maxima of stationary Gaussian processes,” Ann. Probab.,4, No. 3, 357–371 (1976).
C. Nanopoulos and P. Nobelis, “Régularité et propriétés limites des fonctions aléatoires,” Lect. Notes Math.,649, 567–690 (1978).
J. Pickands, III, “Upcrossing probabilities for stationary Gaussian processes,” Trans. Am. Math. Soc.,145, 51–73, Nov. (1969).
L. D. Pitt, “Local times for Gaussian vector fields,” Indiana Univ. Math. J.,27, No. 2, 309–330 (1978).
L. D. Pitt and Lanh Tat Tran, “Local sample path properties of Gaussian fields,” Ann. Probab.,7, No. 3, 477–493 (1979).
R. L. Plackett, “A reduction formula for normal multivariate integrals,” Biometrika,41, No. 3–4, 351–360 (1954).
C. Quails, “The law of the iterated logarithm on arbitrary sequences for stationary Gaussian processes and Brownian motion,” Ann. Probab.,5, No. 5, 724–739 (1977).
Hiroshi Sato and Masami Tanabe, “Level dependence of the variance of the number of level-crossing points of a stationary Gaussian process,” IEEE Trans. Inf. Theory,25, No. 1, 127–129 (1979).
K. Sharpe, “Some properties of the crossings process generated by a stationary χ2 process,” Adv. Appl. Probab.,10, No. 2, 373–391 (1978).
D. Slepian, “The one-sided barrier problem for Gaussian noise,” Bell System Tech. J.,41, No. 2, 463–501 (1962).
M. S. Taqqu, “Weak convergence to fractional Brownian motion and to the Rosenblatt process,” Z. Wahr. Verw. Geb.,31, No. 4, 287–302 (1975).
M. S. Taqqu, “Law of the iterated logarithm for sums of nonlinear functions of Gaussian variables that exhibit a long range dependence,” Z. Wahr. Verw. Geb.,40, 203–238 (1977).
M. S. Taqqu, “A representation for self-similar processes,” Stochast. Process. Appl.,7, No. 1, 55–64 (1978).
M. Weber, “Classes uniformes de processus gaussiens stationnaries,” Lect. Notes Math.,581, 196–256 (1977).
M. Weber, “Classes superieurs de processus gaussiens,” Z. Wahr. Verw. Geb.,42, No. 2, 113–128 (1978).
M. Weber, “Tests integraus pour certaines classes de processus gaussiens stationnaries a trajectoires continues,” C. R. Acad. Sci.,AB287, No. 14, A969-A971 (1978).
M. Weber, “Sur les D-modules asymptotiques des processus strictement stationnaries ergodiques,” Z. Wahr. Verw. Geb.,536, No. 2, 231–240 (1980).
Additional information
Translated from Itogi Nauki i Tekhniki, Seriya Teoriya Veroyatnostei, Matematicheskaya Statistika, Teoreticheskaya Kibernetika, Vol. 19, pp. 155–199, 1982.
Rights and permissions
About this article
Cite this article
Piterbarg, V.I. Gaussian stochastic processes. J Math Sci 23, 2599–2626 (1983). https://doi.org/10.1007/BF01084706
Issue Date:
DOI: https://doi.org/10.1007/BF01084706