论文标题
在平衡的随机环境中，猝灭远程随机步行的不变性原理
Quenched invariance principle for long range random walks in balanced random environments
论文作者
论文摘要
我们通过概率方法建立了一类长期随机步行的猝灭不变性原理（但不一定是相同分布的）均衡的随机环境，其过渡概率从$ x $到$ y $平均可与$ | | x-y | x-y | | x-y |^|^|^|^{ - （d+α）} $（$ nime cartiange in Attry and Arting and Arting and Arting and and and and。缩放过程，并应用了Martingale问题的唯一性，以确定限制过程。
We establish via a probabilistic approach the quenched invariance principle for a class of long range random walks in independent (but not necessarily identically distributed) balanced random environments, with the transition probability from $x$ to $y$ on average being comparable to $|x-y|^{-(d+α)}$ with $α\in (0,2]$. We use the martingale property to estimate exit time from balls and establish tightness of the scaled processes, and apply the uniqueness of the martingale problem to identify the limiting process. When $α\in (0,1)$, our approach works even for non-balanced cases. When $α=2$, under a diffusive with the logarithmic perturbation scaling, we show that the limit of scaled processes is a Brownian motion.
