The Spread Speed of Multiple Catalytic Branching Random Walks  

作　　者：Rong-li LIU 

机构地区：[1]School of Mathematics and Statistics,Beijing Jiaotong University,Beijing 100044,China

出　　处：《Acta Mathematicae Applicatae Sinica》2023年第2期262-292,共31页应用数学学报（英文版）

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

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 Z.If M_(n) is its maximal position at time n,we prove that there is a constantα>0 such that M_(n)/n converges toαalmost surely on the set of infinite number of visits to the set of catalysts.We 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 moment.We also study the limit of(X_(n))as a measure-valued Markov process.For any function f with compact support,we prove a strong law of large numbers for the process X_(n)(f).

关 键 词：catalytic branching random walk invariant measure martingale change of measure spine decomposition 

分 类 号：O211.65[理学—概率论与数理统计]