{"title":"高斯过程在移动非线性边界上最后退出时间的一个极限定理","authors":"Nikita Karagodin","doi":"10.37190/0208-4147.00043","DOIUrl":null,"url":null,"abstract":"We prove a limit theorem on the convergence of the distributions of the scaled last exit time over a slowly moving nonlinear boundary for a class of Gaussian stationary processes. The limit is a double exponential (Gumbel) distribution.","PeriodicalId":48996,"journal":{"name":"Probability and Mathematical Statistics-Poland","volume":"38 9","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2021-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"A limit theorem for the last exit time over a moving nonlinear boundary for a Gaussian process\",\"authors\":\"Nikita Karagodin\",\"doi\":\"10.37190/0208-4147.00043\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove a limit theorem on the convergence of the distributions of the scaled last exit time over a slowly moving nonlinear boundary for a class of Gaussian stationary processes. The limit is a double exponential (Gumbel) distribution.\",\"PeriodicalId\":48996,\"journal\":{\"name\":\"Probability and Mathematical Statistics-Poland\",\"volume\":\"38 9\",\"pages\":\"\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2021-10-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Probability and Mathematical Statistics-Poland\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.37190/0208-4147.00043\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Probability and Mathematical Statistics-Poland","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.37190/0208-4147.00043","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
A limit theorem for the last exit time over a moving nonlinear boundary for a Gaussian process
We prove a limit theorem on the convergence of the distributions of the scaled last exit time over a slowly moving nonlinear boundary for a class of Gaussian stationary processes. The limit is a double exponential (Gumbel) distribution.
期刊介绍：
PROBABILITY AND MATHEMATICAL STATISTICS is published by the Kazimierz Urbanik Center for Probability and Mathematical Statistics, and is sponsored jointly by the Faculty of Mathematics and Computer Science of University of Wrocław and the Faculty of Pure and Applied Mathematics of Wrocław University of Science and Technology. The purpose of the journal is to publish original contributions to the theory of probability and mathematical statistics.
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