ALMOST SURE CENTRAL LIMIT THEOREM FOR BRANCHING RANDOM WALKS IN RANDOM ENVIRONMENT

被引：22

作者：

Nakashima, Makoto ^{[1
]}

机构：

[1] Kyoto Univ, Div Math, Grad Sch Sci, Kyoto 6068502, Japan

来源：

ANNALS OF APPLIED PROBABILITY | 2011年 / 21卷 / 01期

关键词：

Branching random walk; random environment; central limit theorem; linear stochastic evolutions; phase transition; LINEAR STOCHASTIC EVOLUTIONS; DIRECTED POLYMERS; LOCALIZATION; DIFFUSION; DISORDER;

D O I：

10.1214/10-AAP699

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We consider the branching random walks in d-dimensional integer lattice with time-space i.i.d. offspring distributions. Then the normalization of the total population is a nonnegative martingale and it almost surely converges to a certain random variable. When d >= 3 and the fluctuation of environment satisfies a certain uniform square integrability then it is nondegenerate and we prove a central limit theorem for the density of the population in terms of almost sure convergence.

引用

页码：351 / 373

页数：23

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