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General gauge and conditional gauge theorems. (English) Zbl 1017.60086
A conditional gauge theorem was first proved for Brownian motion by K. L. Chung and Z. Zhao [“From Brownian motion to Schrödinger’s equation” (1995; Zbl 0819.60068)]. Recently, such a result was established also for symmetric stable processes by the authors [J. Funct. Anal. 150, No. 1, 204-239 (1997; Zbl 0886.60072)].
In this paper, a general conditional gauge theorem is established for a large class of Markov processes, including Brownian motions with singular drifts and symmetric stable processes. The proof is based on a general gauge theorem, tailored to be applicable to the conditional process. Also, larger classes of functions are introduced, under which these general theorems hold.

MSC:
60J45 Probabilistic potential theory
60J40 Right processes
35J10 Schrödinger operator, Schrödinger equation
47J20 Variational and other types of inequalities involving nonlinear operators (general)
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[33] SEATTLE, WASHINGTON 98195 E-MAIL: zchen@math.washington.edu DEPARTMENT OF MATHEMATICS UNIVERSITY OF ILLINOIS URBANA, ILLINOIS 61801 E-MAIL: rsong@math.uiuc.edu
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