Discrete approximation of symmetric jump processes on metric measure spaces
From the text: ``The paper is concerned with the following two questions. (Q1) Given a symmetric Hunt process \(X\) on \(\mathbb R^d\), can it be approximated by a sequence of symmetric Markov chains \(X^{(k)}\) on \(k^{-1}\mathbb Z^d\)? (Q2) For a sequence \(\{ X^{(k)}:\;k\geq 1\}\) of symmetric Markov chains on \(k^{-1}\mathbb Z^d\), when does \(X^{(k)}\) converge weakly to a `nice' Hunt process \(X\) on \(\mathbb R^d\), as \(k\to \infty\)? In this paper, we address these two questions for symmetric processes \(X\) of pure jump type on a general metric space \(E\)''.
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