Convergence of symmetric Markov chains on \Z^d

2008/07/21 by Richard F. Bass, Takashi Kumagai, Bass, R. F. +3
Mathematics · #60J10 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.0807.3268

openalex publication_date 2008/07/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For each n let Yⁿ_t be a continuous time symmetric Markov chain with state space n^-1 \Z^d. A condition in terms of the conductances is given for the convergence of the Yⁿ_t to a symmetric Markov process Y_t on \R^d. We have weak convergence of \Yⁿ_t: t≤ t₀\ for every t₀ and every starting point. The limit process Y has a continuous part and may also have jumps.

Citations

• A priori Holder estimate, parabolic Harnack principle and heat kernel estimates for diffusions with jumps

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