The Annals of Probability

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

Henry Berbee

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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

Permanent link to this document
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
links.jstor.org

Subjects
Primary: 60G10: Stationary processes
Secondary: 60C05: Combinatorial probability 60K05: Renewal theory

Keywords
Stationary increments point cluster point process

Citation

Berbee, Henry. A Bound on the Size of Point Clusters of a Random Walk with Stationary Increments. Ann. Probab. 11 (1983), no. 2, 414--418. doi:10.1214/aop/1176993606. https://projecteuclid.org/euclid.aop/1176993606


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