Large Deviations of Random Processes Close to Gaussian Ones

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Previous article Next article Large Deviations of Random Processes Close to Gaussian OnesV. I. PiterbargV. I. Piterbarghttps://doi.org/10.1137/1127059PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Yu. K. Belyaeva, Random Processes. Sample Functions and Sections, Mir, Moscow, 1978, (In Russian.) Google Scholar[2] V. I. Piterbarg, Asymptotic expansions for the probabilities of large excursions of Gaussian processes, Dokl. Akad. Nauk SSSR, 242 (1978), 1248–1251, (In Russian.) 80k:60046 Google Scholar[3] V. I. Piterbarg, Comparison of distribution functions of maxima of Gaussian processes, Theory Prob. Appl., 26 (1981), 687–705 0488.60051 LinkGoogle Scholar[4] V. I. Piterbarg, Refinement of a limit theorem for the maximum of a Gaussian stationary processRandom Processes and Fields, MGU, Moscow, 1979, 62–70, (In Russian.) 0546.60040 Google Scholar[5] H. Cramér and , M. Leadbetter, Stationary and related stochastic processes. Sample function properties and their applications, John Wiley & Sons Inc., New York, 1967xii+348 36:949 0162.21102 Google Scholar[6] V. V. Petrov, Sums of independent random variables, Springer-Verlag, New York, 1975x+346 52:9335 0322.60042 CrossrefGoogle Scholar[7] V. Richter, Multi-dimensional local limit theorems for large deviations, Theory Prob. Appl., 3 (1958), 100–106 LinkGoogle Scholar[8] I. Dubinskaite and , A. Karoblis, Local limit theorems for sums of identically distributed random vectors. V, Litovsk. Mat. Sb., 18 (1978), 93–106, 242, (In Russian.) 57:17773 0391.60031 Google Scholar[9] V. I. Piterbarg, Mixing of quantified random processes. VInvestigations in Random Fields, Vol. 50, MGU, Moscow, 1974, 59–78, (In Russian.) Google Scholar[10] Yu. V. Kazachenko, Sufficient conditions for the continuity with probability one of sub-Gaussian random processes, Dopovīdī Akad. Nauk Ukraïn. RSR Ser. A, 1968 (1968), 113–115 37:3640 Google Scholar[11] S. M. Rytov, Introduction to Statistical Radiophysics. Part I. Random Processes, Nauka, Moscow, 1976, (In Russian.) Google Scholar[12] Yu. A. Rozanovm, Stationary Random Processes, Fizmatgiz, Moscow, 1963, (In Russian.) Google Scholar[13] Yu. V. Prokhorov and , Yu. A. Rozanov, Probability Theory, Nauka, Moscow, 1976, (In Russian.) 0463.60001 Google Scholar[14] N. Donald Ylvisaker, On a theorem of Cramér and Leadbetter, Ann. Math. Statist., 37 (1966), 682–685 33:1901 0143.19402 CrossrefGoogle Scholar[15] M. Giné Evarist, On the central limit theorem for sample continuous processes, Ann. Probability, 2 (1974), 629–641 51:6921 CrossrefGoogle Scholar[16] James Pickands, III, Upcrossing probabilities for stationary Gaussian processes, Trans. Amer. Math. Soc., 145 (1969), 51–73 40:3606 0206.18802 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails The winding of stationary Gaussian processes24 November 2017 | Probability Theory and Related Fields, Vol. 172, No. 1-2 Cross Ref On approximating the probability of a large excursion of a nonstationary Gaussian process18 February 2010 | Siberian Mathematical Journal, Vol. 51, No. 1 Cross Ref On excursion sets, tube formulas and maxima of random fieldsThe Annals of Applied Probability, Vol. 10, No. 1 Cross Ref Bounds and asymptotic expansions for the distribution of the Maximum of a smooth stationary Gaussian process15 August 2002 | ESAIM: Probability and Statistics, Vol. 3 Cross Ref On the rate of convergence for extremes of mean square differentiable stationary normal processes14 July 2016 | Journal of Applied Probability, Vol. 34, No. 4 Cross Ref Extreme value theory for stochastic processesScandinavian Actuarial Journal, Vol. 1995, No. 1 Cross Ref Volume 27, Issue 3| 1983Theory of Probability & Its Applications History Submitted:05 February 1980Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1127059Article page range:pp. 504-524ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics