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

Author

Listed:
  • Denis Denisov

    (University of Manchester)

  • Kaiyuan Zhang

    (University of Manchester)

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.

Suggested Citation

  • Denis Denisov & Kaiyuan Zhang, 2025. "Markov Chains in the Domain of Attraction of Brownian Motion in Cones," Journal of Theoretical Probability, Springer, vol. 38(1), pages 1-34, March.
    • Handle: RePEc:spr:jotpro:v:38:y:2025:i:1:d:10.1007_s10959-024-01369-7
    DOI: 10.1007/s10959-024-01369-7
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