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
N1 - Publisher Copyright:
© 2015 American Mathematical Society.
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 - http://www.scopus.com/inward/record.url?scp=84927640176&partnerID=8YFLogxK
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 -