The Annals of Probability

General gauge and conditional gauge theorems

Zhen-Qing Chen and Renming Song

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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.

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Ann. Probab., Volume 30, Number 3 (2002), 1313-1339.

First available in Project Euclid: 20 August 2002

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Primary: 60J45: Probabilistic potential theory [See also 31Cxx, 31D05] 60J40: Right processes
Secondary: 35J10: Schrödinger operator [See also 35Pxx] 47J20: Variational and other types of inequalities involving nonlinear operators (general) [See also 49J40]

Green's function gauge theorem Green function conditional process Kato class conditional gauge theorem


Chen, Zhen-Qing; Song, Renming. General gauge and conditional gauge theorems. Ann. Probab. 30 (2002), no. 3, 1313--1339. doi:10.1214/aop/1029867129.

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