论文标题
关于障碍问题的障碍问题，随机行走时有均匀的随机环境
On the barrier problem of branching random walk in time-inhomogeneous random environment
论文作者
论文摘要
我们考虑在时间抗均匀的随机环境中具有随机吸收屏障的超临界分支随机步行，即，在每一代中，只有出生的障碍物以下的个体才能生存和繁殖。假设随机环境为i.i.d ..屏障设置为$χ_n+an^α，$ a，α$是两个常数，$ \ {χ_n\} $是一个确定的I.I.I.D.由随机环境确定的随机步行。我们表明，对于几乎可以肯定的环境（即，一系列点过程，这是对随机环境的实现），在给定环境下，时间抗均匀的分支随机步行将变为灭绝（sect。如果$α<1/3 $或$α= 1/3，A <1/3，A <a__c $ <a_c $（quest），则可以灭绝积极的概率）。 $α= 1/3，a> a_c $），其中$ a_c $是由随机环境确定的正常数。还获得了$α<\ frac {1} {3}，a \ geq0 $和$α= 1/3的灭绝率，也获得了（0，a_c）$。这些将主要结果扩展到“ \”颁奖典礼（2011年）和贾菲尔（2012），延伸到随机环境案例中。已指定了随机环境所造成的影响。
We consider a supercritical branching random walk in time-inhomogeneous random environment with a random absorption barrier, i.e.,in each generation, only the individuals born below the barrier can survive and reproduce. Assume that the random environment is i.i.d..The barrier is set as $χ_n+an^α,$ where $a,α$ are two constants and $\{χ_n\}$ is a certain i.i.d. random walk determined by the random environment.We show that for almost surely given environment (i.e., a sequence of point processes which is a realization of the random environment), the time-inhomogeneous branching random walk under the given environment will become extinct (resp., survive with positive probability) if $α<1/3$ or $α=1/3, a<a_c$ (resp., $α>1/3, a>0$ or $α=1/3, a>a_c$), where $a_c$ is a positive constant determined by the random environment. The rates of extinction when $α<\frac{1}{3}, a\geq0$ and $α=1/3, a\in(0,a_c)$ are also obtained. These extend the main results in A\"ıdékon $\&$ Jaffuel (2011) and Jaffuel (2012),to the random environment case. The influence caused by the random environment have been specified.
