Stability of Dirichlet heat kernel estimates for non-local operators under Feynman-KAC perturbation

Zhen Qing Chen; Panki Kim; Renming Song

doi:10.1090/S0002-9947-2014-06190-4

Stability of Dirichlet heat kernel estimates for non-local operators under Feynman-KAC perturbation

Zhen Qing Chen
, Panki Kim
, Renming Song

University of Washington
Seoul National University
University of Illinois at Urbana-Champaign

Research output: Contribution to journal › Article › peer-review

22 Citations (Scopus)

Abstract

In this paper we show that Dirichlet heat kernel estimates for a class of (not necessarily symmetric) Markov processes are stable under nonlocal Feynman-Kac perturbations. This class of processes includes, among others, (reflected) symmetric stable-like processes in closed d-sets in Rd, killed symmetric stable processes, censored stable processes in C^1,1 open sets, as well as stable processes with drifts in bounded C^1,1 open sets. These twosided estimates are explicit involving distance functions to the boundary.

Original language	English
Pages (from-to)	5237-5270
Number of pages	34
Journal	Transactions of the American Mathematical Society
Volume	367
Issue number	7
DOIs	https://doi.org/10.1090/S0002-9947-2014-06190-4
Publication status	Published - 1 Jul 2015
Externally published	Yes

Keywords

Censored stable process
Dirichlet heat kernel
Feynman-Kac perturbation
Feynman-Kac transform
Fractional Laplacian
Heat kernel
Relativistic symmetric stable process
Symmetric stablelike process
Symmetric α-stable process
Transition density

Access to Document

10.1090/S0002-9947-2014-06190-4

Cite this

@article{c2cf329220044a898a469b26e2e85bb5,

title = "Stability of Dirichlet heat kernel estimates for non-local operators under Feynman-KAC perturbation",

abstract = "In this paper we show that Dirichlet heat kernel estimates for a class of (not necessarily symmetric) Markov processes are stable under nonlocal Feynman-Kac perturbations. This class of processes includes, among others, (reflected) symmetric stable-like processes in closed d-sets in Rd, killed symmetric stable processes, censored stable processes in C1,1 open sets, as well as stable processes with drifts in bounded C1,1 open sets. These twosided estimates are explicit involving distance functions to the boundary.",

keywords = "Censored stable process, Dirichlet heat kernel, Feynman-Kac perturbation, Feynman-Kac transform, Fractional Laplacian, Heat kernel, Relativistic symmetric stable process, Symmetric stablelike process, Symmetric α-stable process, Transition density",

author = "Chen, \{Zhen Qing\} and Panki Kim and Renming Song",

note = "Publisher Copyright: {\textcopyright} 2015 American Mathematical Society.",

year = "2015",

month = jul,

day = "1",

doi = "10.1090/S0002-9947-2014-06190-4",

language = "English",

volume = "367",

pages = "5237--5270",

journal = "Transactions of the American Mathematical Society",

issn = "0002-9947",

publisher = "American Mathematical Society",

number = "7",

}

TY - JOUR

T1 - Stability of Dirichlet heat kernel estimates for non-local operators under Feynman-KAC perturbation

AU - Chen, Zhen Qing

AU - Kim, Panki

AU - Song, Renming

PY - 2015/7/1

Y1 - 2015/7/1

N2 - In this paper we show that Dirichlet heat kernel estimates for a class of (not necessarily symmetric) Markov processes are stable under nonlocal Feynman-Kac perturbations. This class of processes includes, among others, (reflected) symmetric stable-like processes in closed d-sets in Rd, killed symmetric stable processes, censored stable processes in C1,1 open sets, as well as stable processes with drifts in bounded C1,1 open sets. These twosided estimates are explicit involving distance functions to the boundary.

AB - In this paper we show that Dirichlet heat kernel estimates for a class of (not necessarily symmetric) Markov processes are stable under nonlocal Feynman-Kac perturbations. This class of processes includes, among others, (reflected) symmetric stable-like processes in closed d-sets in Rd, killed symmetric stable processes, censored stable processes in C1,1 open sets, as well as stable processes with drifts in bounded C1,1 open sets. These twosided estimates are explicit involving distance functions to the boundary.

KW - Censored stable process

KW - Dirichlet heat kernel

KW - Feynman-Kac perturbation

KW - Feynman-Kac transform

KW - Fractional Laplacian

KW - Heat kernel

KW - Relativistic symmetric stable process

KW - Symmetric stablelike process

KW - Symmetric α-stable process

KW - Transition density

UR - https://www.scopus.com/pages/publications/84927640176

U2 - 10.1090/S0002-9947-2014-06190-4

DO - 10.1090/S0002-9947-2014-06190-4

M3 - Article

AN - SCOPUS:84927640176

SN - 0002-9947

VL - 367

SP - 5237

EP - 5270

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 7

ER -

Stability of Dirichlet heat kernel estimates for non-local operators under Feynman-KAC perturbation

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this