Regularity of harmonic functions for some Markov chains with unbounded range

2012/02/24 by Fangjun Xu, Xu, Fangjun
Mathematics · #FOS: Mathematics #Geometric Analysis and Curvature Flows #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Spectral Theory in Mathematical Physics #math.PR

paper · pdf · doi:10.48550/arxiv.1202.5361

arxiv created 2012/02/24 · openalex publication_date 2012/02/24 · arxiv updated 2012/02/27 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

We consider a class of continuous time Markov chains on \Z^d. These chains are the discrete space analogue of Markov processes with jumps. Under some conditions, we show that harmonic functions associated with these Markov chains are Hölder continuous.

Citations

• Transition Probabilities for Symmetric Jump Processes

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