Markov chain approximations for nonsymmetric processes

2022/05/02 by Marvin Weidner, Weidner, Marvin
Mathematics · Computer Science · #Markov Chains and Monte Carlo Methods #Stochastic processes and statistical mechanics #Advanced Mathematical Modeling in Engineering

paper · pdf · doi:10.48550/arxiv.2205.00845

Abstract

The aim of this article is to prove that diffusion processes in ℝ^d with a drift can be approximated by suitable Markov chains on n^-1ℤ^d. Moreover, we investigate sufficient conditions on the conductances which guarantee convergence of the associated Markov chains to such Markov processes. Analogous questions are answered for a large class of nonsymmetric jump processes. The proofs of our results rely on regularity estimates for weak solutions to the corresponding nonsymmetric parabolic equations and Dirichlet form techniques.

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