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arXiv · 1801.05887

Uniform Ergodicity for Brownian Motion in a Bounded Convex Set

Jackson Loper
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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.

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Jackson Loper. 2018-01-17. Uniform Ergodicity for Brownian Motion in a Bounded Convex Set. https://doi.org/10.1007/s10959-018-0848-7

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