2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/119483Markov chain approximations of symmetric jump processes are investigated. Tightness results and a central limit theorem are established. Moreover, given the generator of a symmetric jump process with state space $\mathbbm{R}^d$ the approximating Markov chains are constructed explicitly. As a byproduct we obtain a definition of the Sobolev space $H^{α/2}(\mathbbm{R}^d)$, $α\in (0,2)$, that is equivalent to the standard one.36 pagesProbabilityFunctional Analysis60J75, 60F05, 60B10, 60J27, 60G52text