子体几何分布随机环境中分支过程大偏差的渐近局部概率

IF 0.3 Q4 MATHEMATICS, APPLIED

Discrete Mathematics and Applications Pub Date : 2023-03-01 DOI:10.1515/dma-2023-0008

Konstantin Yu. Denisov

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引用次数: 0

摘要

摘要我们考虑了在随机环境η中的分支过程Zn=Xn，1+…+XnZn−1$Z_｛n｝=X_｛n，1｝+\dotsb+X_｛nZ_｛n-1｝｝$，其中η是独立的同分布变量序列，对于固定的η，随机变量Xi，j是独立的，具有几何分布。我们假设相关的随机行走Sn=ξ1+ξ+ξn$S_n=\xi_1+\dotsb+\xi_n$具有正平均μ μ+）和一些μ+。

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Asymptotic local probabilities of large deviations for branching process in random environment with geometric distribution of descendants

Abstract We consider the branching process Zn=Xn,1+⋯+XnZn−1 $ Z_{n} =X_{n, 1} + \dotsb +X_{nZ_{n-1}} $, in random environmentsη, where η is a sequence of independent identically distributedvariables, for fixed η the random variables Xi, j areindependent, have the geometric distribution. We suppose that the associated random walk Sn=ξ1+⋯+ξn $ S_n = \xi_1 + \dotsb + \xi_n $ has positive meanμ,0 < h (μ;μ+) and someμ+.

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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.