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Uniform Ergodicity for Brownian Motion in a Bounded Convex Set

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  • Jackson Loper

    (Columbia University)

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.

Suggested Citation

  • Jackson Loper, 2020. "Uniform Ergodicity for Brownian Motion in a Bounded Convex Set," Journal of Theoretical Probability, Springer, vol. 33(1), pages 22-35, March.
    • Handle: RePEc:spr:jotpro:v:33:y:2020:i:1:d:10.1007_s10959-018-0848-7
    DOI: 10.1007/s10959-018-0848-7
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    References listed on IDEAS

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