Lower deviations for supercritical branching processes with immigration

作     者：Qi SUN Mei ZHANG Qi SUN;Mei ZHANG

作者机构：School of Mathematics and StatisticsBeijing Technology and Business UniversityBeijing 100048China School of Mathematical SciencesLaboratory of Mathematics and Complex SystemsBeijing Normal UniversityBeijing 100875China 

出 版 物：《Frontiers of Mathematics in China》 (中国高等学校学术文摘·数学（英文）)

年 卷 期：2021年第16卷第2期

页      面：567-594页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：This work was supported in part by the National Natural Science Foundation of China(Grant No.11871103) the National Key Research and Development Program of China(No.2020YFA0712900) Research Foundation for Youth Scholars of Beijing Technology and Business University(Grant No.PXM2019_014213_000007) 

主　　题：Supercritical branching processes lower deviations immigration 

摘      要：For a supercritical branching processes with immigration {Zn};it is known that under suitable conditions on the offspring and immigration distributions, Zn/mn converges almost surely to a finite and strictly positive limit, where m is the offspring mean. We are interested in the limiting properties of P(Zn=kn) with kn=o(mn) as n→∞. We give asymptotic behavior of such lower deviation probabilities in both Schröder and Böttcher cases, unifying and extending the previous results for Galton-Watson processes in literature.