Parabolic Harnack inequality and heat kernel estimates for random walks with long range jumps

2007/02/08 by Martin T. Barlow, Richard F. Bass, Barlow, M. T. +3
Mathematics · #60J27 #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.math/0702221

openalex publication_date 2007/02/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the relationships between the parabolic Harnack inequality, heat kernel estimates, some geometric conditions, and some analytic conditions for random walks with long range jumps. Unlike the case of diffusion processes, the parabolic Harnack inequality does not, in general, imply the corresponding heat kernel estimates.

Citations

• Transition Probabilities for Symmetric Jump Processes

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