Limit Theorem for High Levela-Upcrossings by $\chi$-Process

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Previous article Next article Limit Theorem for High Level a-Upcrossings by $\chi$-ProcessV. Piterbarg and S. StamatovicV. Piterbarg and S. Stamatovichttps://doi.org/10.1137/S0040585X97980786PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractThis paper proves the Poisson limit theorem for a number of large excursions of the modulus of the Gaussian vector process with independent identically distributed increments.[1] J. Adler, On excursion sets, tube formulas and maxima of random fields, Ann. Appl. Probab., 10 (2000), pp. 1–74. 9lb ZZZZZZ 1050-5164 Ann. Appl. Probab. CrossrefGoogle Scholar[2] Google Scholar[3] R. Illsley, The excursions of a stationary Gaussian process outside a large two‐dimensional region, Adv. in Appl. Probab., 33 (2001), pp. 141–159. aaz AAPBBD 0001-8678 Adv. Appl. Probab. CrossrefGoogle Scholar[4] Google Scholar[5] Google Scholar[6] Google Scholar[7] Google ScholarKeywordsGaussian processlarge excursion$\chi$-square process Previous article Next article FiguresRelatedReferencesCited ByDetails Almost sure central limit theorems for the maxima of Gaussian functionsCommunications in Statistics - Theory and Methods, Vol. 51, No. 20 | 11 January 2021 Cross Ref High Excursions of a Quadratic form for a Gaussian Stationary Vector ProcessJournal of Mathematical Sciences, Vol. 262, No. 4 | 24 May 2022 Cross Ref High excursions of Bessel and related random processesStochastic Processes and their Applications, Vol. 130, No. 8 | 1 Aug 2020 Cross Ref Method of Moments for Exit Probabilities of Gaussian Vector Processes From a Large RegionA. O. Kleban and V. I. PiterbargTheory of Probability & Its Applications, Vol. 63, No. 4 | 5 February 2019AbstractPDF (200 KB)Большие выбросы процессов гауссовского хаоса. Аппроксимация в дискретном времениТеория вероятностей и ее применения, Vol. 63, No. 1 | 1 Jan 2018 Cross Ref Теория вероятностей и ее применения, Vol. 63, No. 4 | 2018 Cross Ref High Extremes of Gaussian Chaos Processes: A Discrete Time Approximation ApproachA. I. Zhdanov and V. I. PiterbargTheory of Probability & Its Applications, Vol. 63, No. 1 | 24 October 2018AbstractPDF (311 KB)High extrema of Gaussian chaos processesExtremes, Vol. 19, No. 2 | 2 February 2016 Cross Ref Large extremes of Gaussian chaos processesDoklady Mathematics, Vol. 93, No. 2 | 20 May 2016 Cross Ref On Probability of High Extremes for Product of Two Gaussian Stationary ProcessesTheory of Probability & Its Applications, Vol. 60, No. 3 | 15 September 2016AbstractPDF (165 KB)On probability of high extremes for product of two independent Gaussian stationary processesExtremes, Vol. 18, No. 1 | 31 August 2014 Cross Ref Limit laws for the maxima of stationary chi-processes under random indexTEST, Vol. 23, No. 4 | 8 April 2014 Cross Ref Exact asymptotics and limit theorems for supremum of stationary χ -processes over a random intervalStochastic Processes and their Applications, Vol. 123, No. 8 | 1 Aug 2013 Cross Ref Limit theorems for extremes of strongly dependent cyclo-stationary χ-processesExtremes, Vol. 16, No. 2 | 9 February 2013 Cross Ref Cox limit theorem for large excursions of a norm of a Gaussian vector processStatistics & Probability Letters, Vol. 80, No. 19-20 | 1 Oct 2010 Cross Ref Volume 48, Issue 4| 2004Theory of Probability & Its Applications575-752 History Published online:25 July 2006 InformationCopyright © 2004 Society for Industrial and Applied MathematicsKeywordsGaussian processlarge excursion$\chi$-square processPDF Download Article & Publication DataArticle DOI:10.1137/S0040585X97980786Article page range:pp. 734-741ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics