Uniform Ergodicity for Brownian Motion in a Bounded Convex Set
Probability
2022-08-04 v1
Abstract
We consider an n-dimensional Brownian Motion trapped inside a bounded convex set by normally-reflecting boundaries. It is well-known that this process is uniformly ergodic. However, the rates of this ergodicity are not well-understood, especially in the regime of very high-dimensional sets. Here we present new bounds on these rates for convex sets with a given diameter. Our bounds do not depend upon the smoothness of the boundary nor the value of the ambient dimension, n.
Cite
@article{arxiv.1801.05887,
title = {Uniform Ergodicity for Brownian Motion in a Bounded Convex Set},
author = {Jackson Loper},
journal= {arXiv preprint arXiv:1801.05887},
year = {2022}
}