{"title":"High Excursion Probabilities for Gaussian Fields on Smooth Manifolds","authors":"V. I. Piterbarg","doi":"10.1137/s0040585x97t991921","DOIUrl":null,"url":null,"abstract":"Theory of Probability &Its Applications, Volume 69, Issue 2, Page 294-312, August 2024. <br/> Gaussian random fields on finite-dimensional smooth manifolds, whose variance functions reach their maximum values at smooth submanifolds, are considered, and the exact asymptotic behavior of large excursion probabilities is established. It is shown that our conditions on the behavior of the covariation and variance are best possible in the context of the classical Pickands double sum method. Applications of our asymptotic formulas to large deviations of Gaussian vector processes are considered, and some examples are given. This paper continues the previous study of the author with Kobelkov, Rodionov, and Hashorva [J. Math. Sci., 262 (2022), pp. 504--513] which was concerned with Gaussian processes and fields on manifolds with a single point of maximum of the variance.","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":"172 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theory of Probability and its Applications","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/s0040585x97t991921","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0
Abstract
Theory of Probability &Its Applications, Volume 69, Issue 2, Page 294-312, August 2024. Gaussian random fields on finite-dimensional smooth manifolds, whose variance functions reach their maximum values at smooth submanifolds, are considered, and the exact asymptotic behavior of large excursion probabilities is established. It is shown that our conditions on the behavior of the covariation and variance are best possible in the context of the classical Pickands double sum method. Applications of our asymptotic formulas to large deviations of Gaussian vector processes are considered, and some examples are given. This paper continues the previous study of the author with Kobelkov, Rodionov, and Hashorva [J. Math. Sci., 262 (2022), pp. 504--513] which was concerned with Gaussian processes and fields on manifolds with a single point of maximum of the variance.
期刊介绍:
Theory of Probability and Its Applications (TVP) accepts original articles and communications on the theory of probability, general problems of mathematical statistics, and applications of the theory of probability to natural science and technology. Articles of the latter type will be accepted only if the mathematical methods applied are essentially new.