Markov chains in the domain of attraction of Brownian motion in cones

Denis Denisov; Kaiyuan Zhang

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arXiv · 2309.16311

Markov chains in the domain of attraction of Brownian motion in cones

Denis Denisov·Kaiyuan Zhang

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Abstract

We consider a multidimensional Markov Chain $X$ converging to a multidimensional Brownian Motion. We construct a positive harmonic function for $X$ killed on exiting the cone. We show that its asymptotic behavior is similar to that of to the harmonic function of Brownian motion. We use the harmonic function to study the asymptotic behaviour of the tail distribution of the exit time $\tau$ of $X$ from a cone.

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Denis Denisov, Kaiyuan Zhang. 2023-09-28. Markov chains in the domain of attraction of Brownian motion in cones. https://arxiv.org/abs/2309.16311

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