A Bound on the Size of Point Clusters of a Random Walk with Stationary Increments

Abstract

Consider a random walk on $\mathbb{R}^d$ with stationary, possibly dependent increments. Let $N(V)$ count the number of visits to a bounded set $V$. We give bounds on the size of $N(t + V)$, uniformly in $t$, in terms of the behavior of $N$ in a neighborhood of the origin.