The Spread Speed of Multiple Catalytic Branching Random Walks

作     者：Rong-li LIU Rong-li LIU

作者机构：School of Mathematics and StatisticsBeijing Jiaotong UniversityBeijing 100044China 

出 版 物：《Acta Mathematicae Applicatae Sinica》 (应用数学学报（英文版）)

年 卷 期：2023年第39卷第2期

页      面：262-292页

核心收录：

学科分类：02[经济学] 0202[经济学-应用经济学] 020208[经济学-统计学] 07[理学] 0714[理学-统计学（可授理学、经济学学位）] 070103[理学-概率论与数理统计] 0701[理学-数学] 

基　　金：supported in part by the National Natural Science Foundation of China (No.12271374) 

主　　题：catalytic branching random walk invariant measure martingale change of measure spine decomposition 

摘      要：In this paper we study the asymptotic behavior of the maximal position of a supercritical multiple catalytic branching random walk(X_(n))on *** M_(n) is its maximal position at time n,we prove that there is a constantα0 such that M_(n)/n converges toαalmost surely on the set of infinite number of visits to the set of *** also derive the asymptotic law of the centered process M_(n)-αn as n→∞.Our results are similar to those in[13].However,our results are proved under the assumption of finite L log L moment instead of finite second *** also study the limit of(X_(n))as a measure-valued Markov *** any function f with compact support,we prove a strong law of large numbers for the process X_(n)(f).