Heat Kernel Estimates for Non-symmetric Finite Range Jump Processes

作     者：Jie Ming WANG Jie Ming WANG

作者机构：Department of Mathematics and StatisticsBeijing Institute of TechnologyBeijing 100081P.R.China 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2021年第37卷第2期

页      面：229-248页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Partially supported by NSFC(Grant Nos.11731009 and 11401025) 

主　　题：Heat kernel transition density function gradient estimate finite range jump process truncated fractional Laplacian martingale problem 

摘      要：In this paper,we first establish the sharp two-sided heat kernel estimates and the gradient estimate for the truncated fractional Laplacian under gradient perturbation S^(b):=△^(α/2)+b·▽,where △^(α/2) is the truncated fractional Laplacian,α∈(1,2) and b ∈ K_(d)^(α-1).In the second part,for a more general finite range jump process,we present some sufficient conditions to allow that the two sided estimates of the heat kernel are comparable to the Poisson type function for large distance |x-y|in short time.