On the asymptotic normality conditions for the number of repetitions in a stationary random sequence-Reference-Cited by-同舟云学术

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

Published:2022-12-01 Issue:6 Volume:32 Page:391-401
ISSN:0924-9265
Container-title:Discrete Mathematics and Applications
language:en
Short-container-title:

Author:

Mikhailov Vladimir G.¹,Mezhennaya Natalia M.²,Volgin Artem V.³

Affiliation:

1. Steklov Mathematical Institute of Russian Academy of Sciences , Moscow , Russia

2. Bauman Moscow State Technical University , Moscow , Russia

3. MIREA – Russian Technological University , Moscow , Russia

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.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Discrete Mathematics and Combinatorics

Link

https://www.degruyter.com/document/doi/10.1515/dma-2022-0034/pdf

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