Extremum of a time-inhomogeneous branching random walk  

作　　者：Wanting HOU Xiaoyue ZHANG Wenming HONG 

机构地区：[1]Department of Mathematics,Northeastern University,Shenyang 110004,China [2]School of Statistics,Capital University of Economics and Business,Beijing 100070,China [3]School of Mathematical Sciences&Laboratory of Mathematics and Complex Systems,Beijing Normal University,Beijing 100875,China

出　　处：《Frontiers of Mathematics in China》2021年第2期459-478,共20页中国高等学校学术文摘·数学（英文）

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).

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 B>0 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.

关 键 词：Branching random walk time-inhomogeneous branching process random walk 

分 类 号：O17[理学—数学]