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Quasi-Regular Dirichlet Forms: Examples and Counterexamples

Published online by Cambridge University Press:  20 November 2018

Michael Röckner  and
Byron Schmuland
Michael Röckner
Affiliation:
Institut für Angewandte Mathematik Universität Bonn Wegelerstraβe 6 53115 Bonn Germany
Byron Schmuland
Affiliation:
Department of Statistics and Applied Probability University of Alberta Edmonton, Alberta T6G 2G1
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Abstract

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We prove some new results on quasi-regular Dirichlet forms. These include results on perturbations of Dirichlet forms, change of speed measure, and tightness. The tightness implies the existence of an associated right continuous strong Markov process. We also discuss applications to a number of examples including cases with possibly degenerate (sub)-elliptic part, diffusions on loop spaces, and certain Fleming- Viot processes.

Keywords

31C2560J60Dirichlet formsquasi-regularitycapacitiessmooth measuresexceptional setstightnesssquare field operatorM processesdegenerate cases
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 47 , Issue 1 , 01 February 1995 , pp. 165 - 200
Copyright
Copyright © Canadian Mathematical Society 1995

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