{"title":"Moments and asymptotic properties for supercritical branching processes with immigration in random environments","authors":"Chunmao Huang, Chen Wang, Xiaoqiang Wang","doi":"10.1080/15326349.2022.2040365","DOIUrl":null,"url":null,"abstract":"Abstract We consider a supercritical discrete-time branching process with immigration Y in a stationary and ergodic environment ξ. Let mn be the mean of the reproduction distribution at time n conditioned on the environment ξ and be the natural submartingale of the model. We show sufficient conditions for the boundedness of the moments and for and discover the exponential Lp decay rates of as well as the rates of Then, as an application of the moment results, we show the exponential decay rates of and the convergence rates of the average of ratios","PeriodicalId":21970,"journal":{"name":"Stochastic Models","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2022-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Stochastic Models","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1080/15326349.2022.2040365","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 1
Abstract
Abstract We consider a supercritical discrete-time branching process with immigration Y in a stationary and ergodic environment ξ. Let mn be the mean of the reproduction distribution at time n conditioned on the environment ξ and be the natural submartingale of the model. We show sufficient conditions for the boundedness of the moments and for and discover the exponential Lp decay rates of as well as the rates of Then, as an application of the moment results, we show the exponential decay rates of and the convergence rates of the average of ratios
期刊介绍：
Stochastic Models publishes papers discussing the theory and applications of probability as they arise in the modeling of phenomena in the natural sciences, social sciences and technology. It presents novel contributions to mathematical theory, using structural, analytical, algorithmic or experimental approaches. In an interdisciplinary context, it discusses practical applications of stochastic models to diverse areas such as biology, computer science, telecommunications modeling, inventories and dams, reliability, storage, queueing theory, mathematical finance and operations research.
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