%0 Journal Article
%A Rong-li LIU
%T The Spread Speed of Multiple Catalytic Branching Random Walks
%D 2023
%R 10.1007/s10255-023-1046-7
%J 应用数学学报(英文)
%P 262-292
%V 39
%N 2
%X In this paper we study the asymptotic behavior of the maximal position of a supercritical multiple catalytic branching random walk $(X_n)$ on $\mathbb Z$. If $M_n$ is its maximal position at time $n$, we prove that there is a constant $\alpha>0$ such that $M_n/n$ converges to $\alpha$ almost surely on the set of infinite number of visits to the set of catalysts. We also derive the asymptotic law of the centered process $M_n-\alpha n$ as $n\to \infty$. 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 $X_n(f)$.
%U https://applmath.cjoe.ac.cn/jweb_yysxxb_en/CN/10.1007/s10255-023-1046-7