General gauge and conditional gauge theorems

Zhen Qing Chen; Renming Song

doi:10.1214/aop/1029867129

General gauge and conditional gauge theorems

Zhen Qing Chen^*, Renming Song

^*Corresponding author for this work

University of Washington

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

53 Citations (Scopus)

Abstract

General gauge and conditional gauge theorems are established for a large class of (not necessarily symmetric) strong Markov processes, including Brownian motions with singular drifts and symmetric stable processes. Furthermore, new classes of functions are introduced under which the general gauge and conditional gauge theorems hold. These classes are larger than the classical Kato class when the process is Brownian motion in a bounded C^1,1 domain.

Original language	English
Pages (from-to)	1313-1339
Number of pages	27
Journal	Annals of Probability
Volume	30
Issue number	3
DOIs	https://doi.org/10.1214/aop/1029867129
Publication status	Published - Jul 2002
Externally published	Yes

Keywords

Conditional gauge theorem
Gauge theorem
Green's function

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10.1214/aop/1029867129

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abstract = "General gauge and conditional gauge theorems are established for a large class of (not necessarily symmetric) strong Markov processes, including Brownian motions with singular drifts and symmetric stable processes. Furthermore, new classes of functions are introduced under which the general gauge and conditional gauge theorems hold. These classes are larger than the classical Kato class when the process is Brownian motion in a bounded C1,1 domain.",

keywords = "Conditional gauge theorem, Gauge theorem, Green's function",

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

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AB - General gauge and conditional gauge theorems are established for a large class of (not necessarily symmetric) strong Markov processes, including Brownian motions with singular drifts and symmetric stable processes. Furthermore, new classes of functions are introduced under which the general gauge and conditional gauge theorems hold. These classes are larger than the classical Kato class when the process is Brownian motion in a bounded C1,1 domain.

KW - Conditional gauge theorem

KW - Gauge theorem

KW - Green's function

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DO - 10.1214/aop/1029867129

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General gauge and conditional gauge theorems

Abstract

Keywords

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