{"title":"Asymptotic local probabilities of large deviations for branching process in random environment with geometric distribution of descendants","authors":"Konstantin Yu. Denisov","doi":"10.1515/dma-2023-0008","DOIUrl":null,"url":null,"abstract":"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<h+satisfies the right-hand Cramer’s condition Eexp(hξi) < ∞ for, some h+. Under theseassumptions, we find the asymptotic representation for local probabilities P(Zn=⌊exp(θ n)⌋) for θ ∈ [θ1, θ2]⊂</given−names><x> </x><surname>(μ;μ+) and someμ+.","PeriodicalId":11287,"journal":{"name":"Discrete Mathematics and Applications","volume":"33 1","pages":"77 - 86"},"PeriodicalIF":0.3000,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Mathematics and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/dma-2023-0008","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
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+.
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.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
