随机环境中有界跳幅的分枝随机游动  

Branching Random Walks with Bounded Steps in Random Environments

作　　者：张小玥 张美娟[2] ZHANG Xiaoyue;ZHANG Meijuan(School of Statistics,Capital University of Economics and Business,Beijing,100070,China;School of Statistics and Mathematics,Central University of Finance and Economics,Beijing,100081,China)

机构地区：[1]首都经济贸易大学统计学院,北京100070 [2]中央财经大学统计与数学学院,北京100081

出　　处：《应用概率统计》2021年第1期59-68,共10页Chinese Journal of Applied Probability and Statistics

基　　金：国家自然科学基金项目(批准号:11801596、11971062);国家社会科学基金项目(批准号:20BTJ042);首都经济贸易大学北京市属高校基本科研业务费专项资金项目(批准号:XRZ2021035)资助。

摘　　要：考虑随机环境中有界跳幅的分枝随机游动,其中粒子的繁衍构成时间随机环境中的分枝过程,粒子的运动遵循空间随机环境中有界跳幅的随机游动规律.在分枝过程不灭绝的条件下,文章研究n时刻最右粒子位置的极限性质.We consider a branching random walk with bounded steps in random environments,where the particles are produced as a branching process with a random environment in time,and move independently as a random walk with bounded steps on Z with a random environment in location.We study the speed of the rightmost particle,conditionally on the survival of the branching process.

关 键 词：随机环境中分枝过程 随机环境中随机游动 最右粒子 大偏差 

分 类 号：O211.6[理学—概率论与数理统计]