Almost sure central limit theorem for branching random walks in random environment
Almost sure central limit theorem for branching random walks in random environment
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DOI：
10.1214/10-aap699
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发表时间：
2011-01
影响因子：
1.8
通讯作者：
M. Nakashima
中科院分区：
文献类型：
--
作者：
M. Nakashima
我们考虑了具有时空I.I.D.的$d$维整数格中的分枝随机游动。后代分布。则总体的正规化是一个非负鞅，且几乎必然收敛于某个随机变量。当环境涨落满足一定的一致平方可积时，它是非退化的，并证明了种群密度的中心极限定理。
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 $d\geq3$ 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.