Heat kernel estimates for Δ + Δα/2 under gradient perturbation

被引：22

作者：

Chen, Zhen-Qing ^{[1
]}

Hu, Eryan ^{[2
]}

机构：

[1] Univ Washington, Dept Math, Seattle, WA 98195 USA

[2] Beijing Inst Technol, Sch Math & Stat, Beijing 100081, Peoples R China

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2015年 / 125卷 / 07期

基金：

美国国家科学基金会;

关键词：

Heat kernel; Transition density; Feller semigroup; Perturbation; Positivity; Levy system; Kato class; BROWNIAN-MOTION; SINGULAR DRIFT; FRACTIONAL LAPLACIAN; HARNACK INEQUALITY; STABLE PROCESS; SETS;

D O I：

10.1016/j.spa.2015.02.016

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

For alpha is an element of (0, 2) and M > 0, we consider a family of nonlocal operators {Delta + a(alpha) Delta(alpha/2), a is an element of (0, M]} on le under Kato class gradient perturbation. We establish the existence and uniqueness of their fundamental solutions, and derive their sharp two-sided estimates. The estimates give explicit dependence on a and recover the sharp estimates for Brownian motion with drift as a -> 0. Each fundamental solution determines a conservative Feller process X. We characterize X as the unique solution of the corresponding martingale problem as well as a Levy process with singular drift. (C) 2015 Elsevier B.V. All rights reserved.

引用

页码：2603 / 2642

页数：40

共 18 条

[1]

Applebaum D., 2004, Levy Processes and Stochastic Calculus

[2]

Bass RF, 2003, ANN PROBAB, V31, P791

[3]

Blumenthal R. M., 1968, Markov processes and potential theory, V29

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