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.
Publié le : 1983-05-14
Classification:
Stationary increments,
point cluster,
point process,
60G10,
60C05,
60K05
@article{1176993606,
author = {Berbee, Henry},
title = {A Bound on the Size of Point Clusters of a Random Walk with Stationary Increments},
journal = {Ann. Probab.},
volume = {11},
number = {4},
year = {1983},
pages = { 414-418},
language = {en},
url = {http://dml.mathdoc.fr/item/1176993606}
}
Berbee, Henry. A Bound on the Size of Point Clusters of a Random Walk with Stationary Increments. Ann. Probab., Tome 11 (1983) no. 4, pp. 414-418. http://gdmltest.u-ga.fr/item/1176993606/