A Limit Theorem for the Maximum Values of Certain Stochastic Processes

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Previous article Next article A Limit Theorem for the Maximum Values of Certain Stochastic ProcessesH. CramérH. Cramérhttps://doi.org/10.1137/1110012PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1A] V. A. Volkonskii˘ and , Yu. A. Rozanov, Some limit theorems for random functions. I, Theor. Probability Appl., 4 (1959), 178–197, (English translations.) MR0121856 0092.33502 LinkGoogle Scholar[1B] V. A. Volkonskii˘ and , Ju. A. Rozanov, Some limit theorems for random functions. II, Teor. Verojatnost. i Primenen., 6 (1961), 202–215 MR0137141 Google Scholar[2] Simeon M. Berman, A law of large numbers for the maximum in a stationary Gaussian sequence, Ann. Math. Statist., 33 (1962), 93–97 MR0133856 0109.11803 CrossrefGoogle Scholar[3] Harald Cramér, On the maximum of a normal stationary stochastic process, Bull. Amer. Math. Soc., 68 (1962), 512–516 MR0140140 0113.33402 CrossrefGoogle Scholar[4] V. A. Ivanov, On the average number of crossings of a level by sample functions of a stochastic process, Theory Prob. Applications, 5 (1960), 319–323, (English translation.) 10.1137/1105031 0100.34101 LinkGoogle Scholar[5] E. V. Bulinskaya, On the average number of crossings of a level by a stationary Gaussian process, Theory Prob. Applications, 6 (1961), 435–438, (English translation.) 10.1137/1106059 0108.31002 LinkGoogle Scholar[6] D. M. Chibisov, Remarks on N. V. Smirnov's paper entitled “Limit distribution laws for order statistics”, Theory Prob. Applications, 7 (1962), 346–347, (English translation.) Google Scholar[7] Simeon M. Berman, Limit theorems for the maximum term in stationary sequences, Ann. Math. Statist., 35 (1964), 502–516 MR0161365 0122.13503 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Approximations of the boundary crossing probabilities for the maximum of moving weighted sums18 June 2018 | Statistical Papers, Vol. 59, No. 4 Cross Ref Bibliography31 October 2017 Cross Ref Distribution of absolute maximum of mean square differentiable Gaussian stationery process6 May 2017 | Radioelectronics and Communications Systems, Vol. 60, No. 4 Cross Ref Extreme Value Theory1 December 2014 Cross Ref Gumbel Distribution29 September 2014 Cross Ref References and Suggested Reading21 July 2008 Cross Ref Fluctuations in the zeros of differentiable Gaussian processes11 March 2008 | Physical Review E, Vol. 77, No. 3 Cross Ref Gumbel Distribution15 August 2006 Cross Ref Extreme Value Theory15 September 2006 Cross Ref Extremes and upcrossing intensities for P-differentiable stationary processesStochastic Processes and their Applications, Vol. 87, No. 2 Cross Ref On excursion sets, tube formulas and maxima of random fieldsThe Annals of Applied Probability, Vol. 10, No. 1 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. 04 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 Bibliography Cross Ref First passage time and extremum properties of Markov and independent processesJournal of Statistical Physics, Vol. 12, No. 3 Cross Ref Time-revealed convergence properties of normalized maxima in stationary Gaussian processesZeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, Vol. 29, No. 2 Cross Ref Level-crossing problems for random processesIEEE Transactions on Information Theory, Vol. 19, No. 3 Cross Ref Estimating Finite-Time Maxima and Minima of a Stationary Gaussian Ornstein-Uhlenbeck Process by Monte Carlo SimulationJournal of the American Statistical Association, Vol. 63, No. 324 Cross Ref On the Number of Level Crossings by a Gaussian Stochastic Process, IIYu. K. Belyaev17 July 2006 | Theory of Probability & Its Applications, Vol. 12, No. 3AbstractPDF (1023 KB)Maxima of stationary Gaussian processesZeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, Vol. 7, No. 3 Cross Ref Volume 10, Issue 1| 1965Theory of Probability & Its Applications History Submitted:03 September 1964Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1110012Article page range:pp. 126-128ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics