Markov Chains in the Domain of Attraction of Brownian Motion in Cones

Denis Denisov () and Kaiyuan Zhang ()
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Denis Denisov: University of Manchester
Kaiyuan Zhang: University of Manchester

Journal of Theoretical Probability, 2025, vol. 38, issue 1, 1-34

Abstract: 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 behaviour is similar to that of the harmonic function of Brownian motion. We use the harmonic function to study the asymptotic behaviour of the tail distribution of the exit time $$\tau $$ τ of X from a cone.

Keywords: Random walk; Markov chain; Exit time; Harmonic function; Conditioned process; Primary 60G50; Secondary 60G40; 60J45; 60F17 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10959-024-01369-7

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