An integral test for the transience of a Brownian path with limited local time
Probability
2010-04-22 v4 Mathematical Physics
math.MP
Abstract
We study a one-dimensional Brownian motion conditioned on a self-repelling behaviour. Given a nondecreasing positive function f(t), consider the measures mu_t obtained by conditioning a Brownian path so that L_s< f(s), for all s<t, where L_s is the local time spent at the origin by time s. It is shown that the measures mu_t are tight, and that any weak limit of mu_t as t tends to infinity is transient provided that t^{-3/2}f(t) is integrable. We conjecture that this condition is sharp and present a number of open problems.
Keywords
Cite
@article{arxiv.0806.0597,
title = {An integral test for the transience of a Brownian path with limited local time},
author = {Itai Benjamini and Nathanael Berestycki},
journal= {arXiv preprint arXiv:0806.0597},
year = {2010}
}
Comments
3 figures. Some typos corrected.