Green function estimate for censored stable processes

Zhen Qing Chen; Panki Kim

doi:10.1007/s00440-002-0226-2

Green function estimate for censored stable processes

Zhen Qing Chen^*, Panki Kim

^*Corresponding author for this work

University of Washington

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

47 Citations (Scopus)

Abstract

Sharp two-sided estimates for Green functions of censored α-stable process Y in a bounded C^1,1 open set D are obtained, where α ∈ (1, 2). It is shown that the Martin boundary and minimal Martin boundary of Y can all be identified with the Euclidean boundary ∂ D of D. Sharp two-sided estimates for the Martin kernel of Y are also derived.

Original language	English
Pages (from-to)	595-610
Number of pages	16
Journal	Probability Theory and Related Fields
Volume	124
Issue number	4
DOIs	https://doi.org/10.1007/s00440-002-0226-2
Publication status	Published - Dec 2002
Externally published	Yes

Keywords

Capacity
Censored stable process
Green function
Harmonic function
Martin boundary
Martin kernel

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10.1007/s00440-002-0226-2

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abstract = "Sharp two-sided estimates for Green functions of censored α-stable process Y in a bounded C1,1 open set D are obtained, where α ∈ (1, 2). It is shown that the Martin boundary and minimal Martin boundary of Y can all be identified with the Euclidean boundary ∂ D of D. Sharp two-sided estimates for the Martin kernel of Y are also derived.",

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

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AU - Kim, Panki

PY - 2002/12

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N2 - Sharp two-sided estimates for Green functions of censored α-stable process Y in a bounded C1,1 open set D are obtained, where α ∈ (1, 2). It is shown that the Martin boundary and minimal Martin boundary of Y can all be identified with the Euclidean boundary ∂ D of D. Sharp two-sided estimates for the Martin kernel of Y are also derived.

AB - Sharp two-sided estimates for Green functions of censored α-stable process Y in a bounded C1,1 open set D are obtained, where α ∈ (1, 2). It is shown that the Martin boundary and minimal Martin boundary of Y can all be identified with the Euclidean boundary ∂ D of D. Sharp two-sided estimates for the Martin kernel of Y are also derived.

KW - Capacity

KW - Censored stable process

KW - Green function

KW - Harmonic function

KW - Martin boundary

KW - Martin kernel

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U2 - 10.1007/s00440-002-0226-2

DO - 10.1007/s00440-002-0226-2

M3 - Article

AN - SCOPUS:0036882783

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VL - 124

SP - 595

EP - 610

JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

IS - 4

ER -

Green function estimate for censored stable processes

Abstract

Keywords

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