General gauge and conditional gauge theorems
type: Item
instance of: scholarly article
title: General gauge and conditional gauge theorems
zbMATH Open document ID: 1017.60086
author: Zhen-Qing Chen
author: Renming Song
published in: The Annals of Probability
publication date: 2003-05-06T00:00:00Z
review text: A conditional gauge theorem was first proved for Brownian motion by \textit{K. L. Chung} and \textit{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.
Mathematics Subject Classification ID: 60J45
Mathematics Subject Classification ID: 60J40
Mathematics Subject Classification ID: 35J10
Mathematics Subject Classification ID: 47J20
zbMATH DE Number: 1906087
zbMATH Keywords: Green's function
zbMATH Keywords: gauge theorem
zbMATH Keywords: conditional gauge theorem
reviewed by: Liliana Popa
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1029867129
OpenAlex ID: W2138808782
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DOI: 10.1214/AOP/1029867129
description: scientific article; zbMATH DE number 1906087