Extremum of a time-inhomogeneous branching random walk

作     者：Wanting HOU Xiaoyue ZHANG Wenming HONG Wanting HOU;Xiaoyue ZHANG;Wenming HONG

作者机构：Department of MathematicsNortheastern UniversityShenyang 110004China School of StatisticsCapital University of Economics and BusinessBeijing 100070China School of Mathematical Sciences&Laboratory 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：459-478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 by the National Key Research and Development Program of China(No.2020YFA0712900) the National Natural Science Foundation of China(Grant NO.11971062) the Fundamental Research Funds for the Central Universities Grant(No.N180503019) 

主　　题：Branching random walk time-inhomogeneous branching process random walk 

摘      要：Consider a time-inhomogeneous branching random walk, generated by the point process Ln which composed by two independent parts: ‘branching’offspring Xn with the mean 1+B(1+n)−β for β∈(0,1) and ‘displacement’ ξn with a drift A(1+n)^(−2α) for α∈(0,1/2), where the ‘branching’ process is supercritical for B0 but ‘asymptotically critical’ and the drift of the ‘displacement’ ξn is strictly positive or negative for |A|0 but ‘asymptotically’ goes to zero as time goes to infinity. We find that the limit behavior of the minimal (or maximal) position of the branching random walk is sensitive to the ‘asymptotical’ parameter β and α.