随机环境中分枝随机游动的极限定理  

Limit Theorems of Branching Random Walks in Random Environments

作　　者：胡杨利[1] 李应求[1] 

机构地区：[1]长沙理工大学数学与计算科学学院

出　　处：《应用数学学报》2015年第2期317-329,共13页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(11771021;11171044);湖南省自然科学基金(13JJ6048;11JJ2001);湖南省高等学校科研基金(14B010)资助项目

摘　　要：在随机环境中分枝随机游动模型中,粒子的繁衍机制是随机环境中分枝过程,各代粒子在直线上的位置由依赖随机环境的点过程给定,讨论了各代点过程的Laplace变换由其条件期望规范化后的极限性质.In this paper, we consider a branching random walk in an independent and identically random environment which controls the probability distribution and the posi- tions of offspring. In this model, the positions of each generation particles is given by a point process. The Laplace transform of all these point processes normalized by their own conditional expectations is a martingale. Here it is shown that under certain conditions, the martingale converges uniformly in some appropriate region, almost surely and in mean.

关 键 词：随机环境 分枝随机游动 一致收敛 几乎处处收敛 依均值收敛 

分 类 号：O211.65[理学—概率论与数理统计]