{"title":"Large deviations of branching process in a random environment","authors":"A. V. Shklyaev","doi":"10.1515/dma-2021-0025","DOIUrl":null,"url":null,"abstract":"Abstract In this first part of the paper we find the asymptotic formulas for the probabilities of large deviations of the sequence defined by the random difference equation Yn+1=AnYn + Bn, where A1, A2, … are independent identically distributed random variables and Bn may depend on {(Ak,Bk),0⩽k<n} $ \\{(A_k,B_k),0\\leqslant k \\lt n\\} $ for any n≥1. In the second part of the paper this results are applied to the large deviations of branching processes in a random environment.","PeriodicalId":11287,"journal":{"name":"Discrete Mathematics and Applications","volume":"31 1","pages":"281 - 291"},"PeriodicalIF":0.3000,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Mathematics and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/dma-2021-0025","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: 4
Abstract
Abstract In this first part of the paper we find the asymptotic formulas for the probabilities of large deviations of the sequence defined by the random difference equation Yn+1=AnYn + Bn, where A1, A2, … are independent identically distributed random variables and Bn may depend on {(Ak,Bk),0⩽k
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.
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