Heat kernel for reflected jump diffusion on Ahlfors regular domains

arXiv (Cornell University) 2026 Preprint Open access

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Authors: Shiping Cao, Zhen-Qing Chen
DOI: 10.48550/arxiv.2602.10448
Cited by: 0

Abstract

We study reflected jump diffusions on Ahlfors regular domains in general metric measure spaces. Under the condition that the Dirichlet form on the ambient space satisfies a capacity upper bound estimate, we construct an extension operator from the reflected Dirichlet space to the ambient Dirichlet space, with a scale-invariant local bound. Second, we establish the mixed stable-like heat kernel estimates for the reflected jump diffusion, assuming that the process on the ambient space satisfies the same type of heat kernel estimates.

Fields of Study & Subjects

Geometric Analysis and Curvature Flows Stochastic processes and statistical mechanics Advanced Harmonic Analysis Research

Publication details

Journal / source
arXiv (Cornell University)
Publication date
11 February 2026
Language
EN
Document type
Preprint