Convergence of symmetric Markov chains on ${\mathbb{Z}}^d$

Abstract

For each $n$ let $Y_t^n$ be a continuous time symmetric Markov chain with state space $n^{-1}{\mathbb{Z}}^d$. A condition in terms of the conductances is given for the convergence of the $Y_t^n$ to a symmetric Markov process $Y_t$ on ${\mathbb{R}}^d$. We have weak convergence of $\{Y_t^n:t\le t_0\}$ for every $t_0$ and every starting point. The limit process $Y$ has a continuous part and may also have jumps.

References in corpus (1)

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

Cited by in corpus (1)

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