Work

Dirichlet heat kernel estimates for a large class of anisotropic Markov processes

Year: 2025

Type: article

Abstract: Let Z=(Z1,…,Zd) be the d-dimensional Lévy process where Zi’s are independent 1-dimensional Lévy processes with identical jumping kernel ν1(r)=r−1ϕ(r)−1. Here ϕ is an increasing function with weakly scaling condition of order α_,α‾∈(0,2). We consider a symmetric function J(x,y) comparable to ν1(|xi−yi|)ifxi≠yifor someiandxj=yjfor allj≠i0ifxi≠yifor more than one indexi. Corresponding to the jumping kernel J, there exists an anisotropic Markov process X, see [32]. In this article, we establish sharp two-sided Dirichlet heat kernel estimates for X in C1,1 open set, under certain regularity conditions. As an application of the main results, we derive the Green function estimates.

Source: Electronic Journal of Probability

DOI: 10.1214/25-ejp1379

Authors: Kyung-Youn Kim, Lidan Wang

Institutions: National Chung Hsing University, Nankai University

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $675

Funders: National Natural Science Foundation of China, National Science and Technology Council