Two-sided heat kernel estimates for censored stable-like processes

Zhen Qing Chen; Panki Kim; Renming Song

doi:10.1007/s00440-008-0193-3

Two-sided heat kernel estimates for censored stable-like processes

Zhen Qing Chen, Panki Kim^*, Renming Song

^*Corresponding author for this work

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

56 Citations (Scopus)

Abstract

In this paper, we study the precise behavior of the transition density functions of censored (resurrected) α-stable-like processes in C^1,1 open sets in ℝ^d, where d ≥ 1 and α ε (1, 2). We first show that the semigroup of the censored α-stable-like process in any bounded Lipschitz open set is intrinsically ultracontractive. We then establish sharp two-sided estimates for the transition density functions of a large class of censored α-stable-like processes in C^1,1 open sets. We further obtain sharp two-sided estimates for the Green functions of these censored α-stable-like processes in bounded C^1,1 open sets.

Original language	English
Pages (from-to)	361-399
Number of pages	39
Journal	Probability Theory and Related Fields
Volume	146
Issue number	3
DOIs	https://doi.org/10.1007/s00440-008-0193-3
Publication status	Published - Dec 2009
Externally published	Yes

Keywords

Boundary Harnack principle
Censored stable process
Censored stable-like process
Exit time
Fractional Laplacian
Green function
Heat kernel
Intrinsic ultracontractivity
Lévy system
Parabolic Harnack principle
Symmetric stable-like process
Symmetric α-stable process
Transition density
Transition density function

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10.1007/s00440-008-0193-3

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title = "Two-sided heat kernel estimates for censored stable-like processes",

abstract = "In this paper, we study the precise behavior of the transition density functions of censored (resurrected) α-stable-like processes in C1,1 open sets in ℝd, where d ≥ 1 and α ε (1, 2). We first show that the semigroup of the censored α-stable-like process in any bounded Lipschitz open set is intrinsically ultracontractive. We then establish sharp two-sided estimates for the transition density functions of a large class of censored α-stable-like processes in C1,1 open sets. We further obtain sharp two-sided estimates for the Green functions of these censored α-stable-like processes in bounded C1,1 open sets.",

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

year = "2009",

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doi = "10.1007/s00440-008-0193-3",

language = "English",

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T1 - Two-sided heat kernel estimates for censored stable-like processes

AU - Chen, Zhen Qing

AU - Kim, Panki

AU - Song, Renming

PY - 2009/12

Y1 - 2009/12

N2 - In this paper, we study the precise behavior of the transition density functions of censored (resurrected) α-stable-like processes in C1,1 open sets in ℝd, where d ≥ 1 and α ε (1, 2). We first show that the semigroup of the censored α-stable-like process in any bounded Lipschitz open set is intrinsically ultracontractive. We then establish sharp two-sided estimates for the transition density functions of a large class of censored α-stable-like processes in C1,1 open sets. We further obtain sharp two-sided estimates for the Green functions of these censored α-stable-like processes in bounded C1,1 open sets.

AB - In this paper, we study the precise behavior of the transition density functions of censored (resurrected) α-stable-like processes in C1,1 open sets in ℝd, where d ≥ 1 and α ε (1, 2). We first show that the semigroup of the censored α-stable-like process in any bounded Lipschitz open set is intrinsically ultracontractive. We then establish sharp two-sided estimates for the transition density functions of a large class of censored α-stable-like processes in C1,1 open sets. We further obtain sharp two-sided estimates for the Green functions of these censored α-stable-like processes in bounded C1,1 open sets.

KW - Boundary Harnack principle

KW - Censored stable process

KW - Censored stable-like process

KW - Exit time

KW - Fractional Laplacian

KW - Green function

KW - Heat kernel

KW - Intrinsic ultracontractivity

KW - Lévy system

KW - Parabolic Harnack principle

KW - Symmetric stable-like process

KW - Symmetric α-stable process

KW - Transition density

KW - Transition density function

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DO - 10.1007/s00440-008-0193-3

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SP - 361

EP - 399

JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

IS - 3

ER -

Two-sided heat kernel estimates for censored stable-like processes

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Keywords

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