Convergence of symmetric Markov chains on ℤd

Abstract

For each n let Yt(n) be a continuous time symmetric Markov chain with state space n-1ℤd. Conditions in terms of the conductances are given for the convergence of the Yt(n)t to a symmetric Markov process Yt on ℝd. We have weak convergence of {Yt(n)}: t ≤ t0} for every t0 and every starting point. The limit process Y has a continuous part and may also have jumps. © 2009 Springer-Verlag.