具有子体几何分布的随机环境中分支过程低偏差的渐近局部概率

IF 0.3 Q4 MATHEMATICS, APPLIED

Discrete Mathematics and Applications Pub Date : 2022-10-01 DOI:10.1515/dma-2022-0026

Konstantin Yu. Denisov

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引用次数: 1

摘要

我们考虑随机环境η中分支过程Zn=Xn,1+⋯+Xn,Zn−1 ${{Z}_{n}}={{X}_{n,1}}+\cdots +{{X}_{n,{{Z}_{n-1}}}}$的低偏差局部概率。我们假设相关随机漫步Sn=ξ1+⋯+ξn ${{S}_{n}}={{\xi }_{1}}+\cdots +{{\xi }_{n}}$具有正均值μ，并且对于某些h−<−1，满足左手克莱默条件exp(hξi)<∞，如果h−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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Asymptotical local probabilities of lower deviations for branching process in random environment with geometric distributions of descendants

Abstract We consider local probabilities of lower deviations for branching process Zn=Xn,1+⋯+Xn,Zn−1 ${{Z}_{n}}={{X}_{n,1}}+\cdots +{{X}_{n,{{Z}_{n-1}}}}$in random environment η. We assume that η is a sequence of independent identically distributed random variables and for fixed environment η the distributions of variables Xi,j are geometric ones.We suppose that the associated random walk Sn=ξ1+⋯+ξn ${{S}_{n}}={{\xi }_{1}}+\cdots +{{\xi }_{n}}$has positive mean μ and satisfies left-hand Cramer’s condition Eexp(hξi)<∞ if h−

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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.