Discrete approximation of reflected Brownian motions by Markov chains on partitions of domains

Hino, Masanori; Maki, Arata; Matsuura, Kouhei

doi:10.1090/tran/9484

Discrete approximation of reflected Brownian motions by Markov chains on partitions of domains
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by Masanori Hino, Arata Maki and Kouhei Matsuura;

Trans. Amer. Math. Soc.

DOI: https://doi.org/10.1090/tran/9484

Published electronically: June 6, 2025

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Abstract:

In this paper, we study discrete approximation of reflected Brownian motions on domains in Euclidean space. Our approximation is given by a sequence of Markov chains on partitions of the domain, where we allow uneven or random partitions. We provide sufficient conditions for the weak convergence of the Markov chains.

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Discrete approximation of reflected Brownian motions by Markov chains on partitions of domains
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Abstract: