Markov chain approximations for symmetric jump processes

2006/11/30 by Ryad Husseini, Moritz Kaßmann, Husseini, R. +1
Economics, Econometrics and Finance · Mathematics · #60B10 #60F05 #60G52 #60J27 #60J75 #FOS: Mathematics #Functional Analysis (math.FA) #Probability (math.PR) #Spectral Theory in Mathematical Physics #Stochastic processes and financial applications #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.math/0611934

openalex publication_date 2006/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Markov 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 \mathbbmR^d the approximating Markov chains are constructed explicitly. As a byproduct we obtain a definition of the Sobolev space H^α/2(\mathbbmR^d), α∈ (0,2), that is equivalent to the standard one.

Citations

• Transition Probabilities for Symmetric Jump Processes

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