## The Annals of Probability

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

Henry Berbee

#### 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.

#### Article information

Source
Ann. Probab., Volume 11, Number 2 (1983), 414-418.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176993606

Digital Object Identifier
doi:10.1214/aop/1176993606

Mathematical Reviews number (MathSciNet)
MR690138

Zentralblatt MATH identifier
0494.60038

JSTOR