Work

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

Year: 2024

Type: article

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.

Source: Journal of Theoretical Probability

DOI: 10.1007/s10959-024-01369-7

Authors: Denis Denisov, Kaiyuan Zhang

Institution: University of Manchester

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funder: Leverhulme Trust