Flux and lateral conditions for symmetric Markov processes

Zhen Qing Chen; Masatoshi Fukushima

doi:10.1007/s11118-008-9097-1

Flux and lateral conditions for symmetric Markov processes

Zhen Qing Chen^*, Masatoshi Fukushima

^*Corresponding author for this work

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

5 Citations (Scopus)

Abstract

The purpose of this paper is to give an affirmative answer at infinitesimal generator level to the 40 years old Feller's boundary problem for symmetric Markov processes with general quasi-closed boundaries. For this, we introduce a new notion of flux functional, which can be intrinsically defined via the minimal process X ⁰ in the interior. We then use it to characterize the L ²-infinitesimal generator of a symmetric process that extends X ⁰. Special attention is paid to the case when the boundary consists of countable many points possessing no accumulation points.

Original language	English
Pages (from-to)	241-269
Number of pages	29
Journal	Potential Analysis
Volume	29
Issue number	3
DOIs	https://doi.org/10.1007/s11118-008-9097-1
Publication status	Published - Nov 2008
Externally published	Yes

Keywords

Boundary
Boundary theory
Extension process
Feller measures
Flux
Infinitesimal generator
Jumping measure
Killing measure
Lateral condition
Martingale
Reflected Dirichlet space
Skew Brownian motion
Symmetric Markov process

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10.1007/s11118-008-9097-1

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abstract = "The purpose of this paper is to give an affirmative answer at infinitesimal generator level to the 40 years old Feller's boundary problem for symmetric Markov processes with general quasi-closed boundaries. For this, we introduce a new notion of flux functional, which can be intrinsically defined via the minimal process X 0 in the interior. We then use it to characterize the L 2-infinitesimal generator of a symmetric process that extends X 0. Special attention is paid to the case when the boundary consists of countable many points possessing no accumulation points.",

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doi = "10.1007/s11118-008-9097-1",

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AU - Fukushima, Masatoshi

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N2 - The purpose of this paper is to give an affirmative answer at infinitesimal generator level to the 40 years old Feller's boundary problem for symmetric Markov processes with general quasi-closed boundaries. For this, we introduce a new notion of flux functional, which can be intrinsically defined via the minimal process X 0 in the interior. We then use it to characterize the L 2-infinitesimal generator of a symmetric process that extends X 0. Special attention is paid to the case when the boundary consists of countable many points possessing no accumulation points.

AB - The purpose of this paper is to give an affirmative answer at infinitesimal generator level to the 40 years old Feller's boundary problem for symmetric Markov processes with general quasi-closed boundaries. For this, we introduce a new notion of flux functional, which can be intrinsically defined via the minimal process X 0 in the interior. We then use it to characterize the L 2-infinitesimal generator of a symmetric process that extends X 0. Special attention is paid to the case when the boundary consists of countable many points possessing no accumulation points.

KW - Boundary

KW - Boundary theory

KW - Extension process

KW - Feller measures

KW - Flux

KW - Infinitesimal generator

KW - Jumping measure

KW - Killing measure

KW - Lateral condition

KW - Martingale

KW - Reflected Dirichlet space

KW - Skew Brownian motion

KW - Symmetric Markov process

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DO - 10.1007/s11118-008-9097-1

M3 - Article

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SN - 0926-2601

VL - 29

SP - 241

EP - 269

JO - Potential Analysis

JF - Potential Analysis

IS - 3

ER -

Flux and lateral conditions for symmetric Markov processes

Abstract

Keywords

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