论文标题
在出生和死亡的动态环境中随机行走
Random walk in a birth-and-death dynamical environment
论文作者
论文摘要
我们将连续移动的粒子视为马尔可夫跳跃过程。它的离散链由$ {\ mathbb z}^d $上的普通随机步行给出，其跳速率为$（{\ mathbf x}，t），t）$由固定功能的固定功能$φ$ $ \\\\\\\\\\\\\\\\\\\\不同站点的BD过程是独立的，并且分布相同，并且$φ$被认为无限限度不增加和消失。当环境“强烈终止”时，我们为粒子位置得出了LLN和CLT。在没有可行的均匀下限的情况下，我们求助于随机统治，以及一个次级参数，以控制粒子在$ n $跳跃中花费的时间；我们还对初始（产品）环境初始分布施加条件。我们还介绍了粒子看到的环境渐近学的结果（在$φ$的不同条件下）。
We consider a particle moving in continuous time as a Markov jump process; its discrete chain is given by an ordinary random walk on ${\mathbb Z}^d$ , and its jump rate at $({\mathbf x},t)$ is given by a fixed function $φ$ of the state of a birth-and-death (BD) process at $\\mathbf x$ on time $t$; BD processes at different sites are independent and identically distributed, and $φ$ is assumed non increasing and vanishing at infinity. We derive a LLN and a CLT for the particle position when the environment is 'strongly ergodic'. In the absence of a viable uniform lower bound for the jump rate, we resort instead to stochastic domination, as well as to a subadditive argument to control the time spent by the particle to give $n$ jumps; and we also impose conditions on the initial (product) environmental initial distribution. We also present results on the asymptotics of the environment seen by the particle (under different conditions on $φ$).
