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Some limit theorems on branching random walks in random environments
Received date: 2010-04-12
Revised date: 2010-06-14
Online published: 2011-05-15
Suppose {Zn;n=0,1,2,…} is a branching random walk in the random environment, and ξ ={ξ0,ξ1,ξ2, …} is the environment process. Let Z(n,x) be the number of the nth generation located in the interval (-∞, x], fξn(s)=∑∞j=0 pξn(j)sj be the generating function of the distribution of the particle in the nth generation, and mξn=fξn' (1). We show that under the specific conditions, there exists a sequence of random variables {tn}, so that Z(n,tn)(∏i=0n-1mξi)-1 converges in L2. For branching random walks in varying environments, we have similar results.
FANG Liang , HU Xiao-Yu . Some limit theorems on branching random walks in random environments[J]. Journal of University of Chinese Academy of Sciences, 2011 , 28(3) : 288 -297 . DOI: 10.7523/j.issn.2095-6134.2011.3.002
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