超过高斯静态序列高水平的点过程的渐近行为

IF 0.2 Q4 MATHEMATICS Moscow University Mathematics Bulletin Pub Date : 2024-03-24 DOI:10.3103/s0027132223060050

V. I. Piterbarg

{"title":"超过高斯静态序列高水平的点过程的渐近行为","authors":"V. I. Piterbarg","doi":"10.3103/s0027132223060050","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The paper studies the asymptotic behavior of point processes of exits of a Gaussian stationary sequence beyond a level tending to infinity more slowly than in the Poisson limit theorem for the number of exits. Convergence in variation of such point processes to a marked Poisson process is proved. The results of Yu.V. Prokhorov on the best approximation of the Bernoulli distribution by a mixture of Gaussian and Poisson distributions are applied. A.N. Kolmogorov proposed this problem in the early 1950s.</p>","PeriodicalId":42963,"journal":{"name":"Moscow University Mathematics Bulletin","volume":null,"pages":null},"PeriodicalIF":0.2000,"publicationDate":"2024-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Asymptotic Behavior of Point Processes of Exceeding the High Levels of Gaussian Stationary Sequence\",\"authors\":\"V. I. Piterbarg\",\"doi\":\"10.3103/s0027132223060050\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<h3 data-test=\\\"abstract-sub-heading\\\">Abstract</h3><p>The paper studies the asymptotic behavior of point processes of exits of a Gaussian stationary sequence beyond a level tending to infinity more slowly than in the Poisson limit theorem for the number of exits. Convergence in variation of such point processes to a marked Poisson process is proved. The results of Yu.V. Prokhorov on the best approximation of the Bernoulli distribution by a mixture of Gaussian and Poisson distributions are applied. A.N. Kolmogorov proposed this problem in the early 1950s.</p>\",\"PeriodicalId\":42963,\"journal\":{\"name\":\"Moscow University Mathematics Bulletin\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.2000,\"publicationDate\":\"2024-03-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Moscow University Mathematics Bulletin\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3103/s0027132223060050\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Moscow University Mathematics Bulletin","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3103/s0027132223060050","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

摘要本文研究了高斯静止序列的出口点过程的渐近行为，其超越水平趋向无穷大的速度比出口数量的泊松极限定理更慢。证明了这种点过程在变化中收敛于有标记的泊松过程。应用了 Yu.V. Prokhorov 关于用高斯分布和泊松分布的混合物对伯努利分布进行最佳逼近的结果。科尔莫戈罗夫（A.N. Kolmogorov）在二十世纪五十年代初提出了这一问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Asymptotic Behavior of Point Processes of Exceeding the High Levels of Gaussian Stationary Sequence

Abstract

The paper studies the asymptotic behavior of point processes of exits of a Gaussian stationary sequence beyond a level tending to infinity more slowly than in the Poisson limit theorem for the number of exits. Convergence in variation of such point processes to a marked Poisson process is proved. The results of Yu.V. Prokhorov on the best approximation of the Bernoulli distribution by a mixture of Gaussian and Poisson distributions are applied. A.N. Kolmogorov proposed this problem in the early 1950s.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Moscow University Mathematics Bulletin MATHEMATICS-

CiteScore

0.60

自引率

25.00%

发文量

期刊介绍： Moscow University Mathematics Bulletin is the journal of scientific publications reflecting the most important areas of mathematical studies at Lomonosov Moscow State University. The journal covers research in theory of functions, functional analysis, algebra, geometry, topology, ordinary and partial differential equations, probability theory, stochastic processes, mathematical statistics, optimal control, number theory, mathematical logic, theory of algorithms, discrete mathematics and computational mathematics.