On the asymptotic normality conditions for the number of repetitions in a stationary random sequence

IF 0.3 Q4 MATHEMATICS, APPLIED

Discrete Mathematics and Applications Pub Date : 2022-12-01 DOI:10.1515/dma-2022-0034

V. Mikhailov, N. Mezhennaya, A. Volgin

引用次数: 0

Abstract

Abstract We study conditions of the asymptotic normality of the number of repetitions (pairs of equal values) in a segment of strict sense stationary random sequence of values from {1, 2, …, N} satisfying the strong uniform mixing condition. It is shown that under natural conditions for the number of repetitions to be asymptotically normal as the length of the segment tends to infinity it is necessary for the stationary distribution to be different from the equiprobable one. Under additional conditions the accuracy of the normal approximation in the uniform metrics is estimated.

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平稳随机序列中重复次数的渐近正态性条件

摘要我们研究了严格意义平稳随机序列{1,2，…，N}中满足强均匀混合条件的重复次数（等值对）的渐近正态性条件。结果表明，在自然条件下，当区间长度趋于无穷大时，重复次数渐近正态，平稳分布与等概率分布不同是必要的。在附加条件下，估计了均匀度量中正态近似的精度。

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

Discrete Mathematics and Applications MATHEMATICS, APPLIED-

CiteScore

0.60

自引率

20.00%

发文量

期刊介绍： The aim of this journal is to provide the latest information on the development of discrete mathematics in the former USSR to a world-wide readership. The journal will contain papers from the Russian-language journal Diskretnaya Matematika, the only journal of the Russian Academy of Sciences devoted to this field of mathematics. Discrete Mathematics and Applications will cover various subjects in the fields such as combinatorial analysis, graph theory, functional systems theory, cryptology, coding, probabilistic problems of discrete mathematics, algorithms and their complexity, combinatorial and computational problems of number theory and of algebra.