Survival and Growth of a Branching Random Walk in Random Environment
Survival and Growth of a Branching Random Walk in Random Environment
复制标题
随机环境中分支随机游走的生存和增长
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
M. Kochler
中科院分区：
文献类型：
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作者：
C. Bartsch;N. Gantert;M. Kochler
我们考虑一个特殊的分支随机游动在随机环境（BRWRE）上的$\sN_0$开始于一个粒子在原点。粒子根据后代分布（取决于位置）繁殖，并向右移动一步（概率为$（0，1]$，也取决于位置）或停留在同一个地方。我们给出了局部和全局生存的准则，并证明了全局生存等价于指数增长的时刻。此外，在生存的情况下，粒子的数量几乎肯定以与矩相同的增长率以指数方式快速增长。
We consider a particular Branching Random Walk in Random Environment (BRWRE) on $\sN_0$ started with one particle at the origin. Particles reproduce according to an offspring distribution (which depends on the location) and move either one step to the right (with a probability in $(0,1]$ which also depends on the location) or stay in the same place. We give criteria for local and global survival and show that global survival is equivalent to exponential growth of the moments. Further, on the event of survival the number of particles grows almost surely exponentially fast with the same growth rate as the moments.