The Annals of Probability

General gauge and conditional gauge theorems

Zhen-Qing Chen and Renming Song

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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 $C^{1,1}$ domain.

Article information

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

Dates
First available: 20 August 2002

Permanent link to this document
http://projecteuclid.org/euclid.aop/1029867129

Digital Object Identifier
doi:10.1214/aop/1029867129

Mathematical Reviews number (MathSciNet)
MR1920109

Zentralblatt MATH identifier
1017.60086

Subjects
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]

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

Citation

Chen, Zhen-Qing; Song, Renming. General gauge and conditional gauge theorems. The Annals of Probability 30 (2002), no. 3, 1313--1339. doi:10.1214/aop/1029867129. http://projecteuclid.org/euclid.aop/1029867129.


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  • SEATTLE, WASHINGTON 98195 E-MAIL: zchen@math.washington.edu DEPARTMENT OF MATHEMATICS UNIVERSITY OF ILLINOIS
  • URBANA, ILLINOIS 61801 E-MAIL: rsong@math.uiuc.edu