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

IF 0.2 Q4 MATHEMATICS

Moscow University Mathematics Bulletin Pub Date : 2024-03-24 DOI:10.3103/s0027132223060050

V. I. Piterbarg

引用次数: 0

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.

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超过高斯静态序列高水平的点过程的渐近行为

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。

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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.