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Markov Processes Associated With Positivity Preserving Coercive Forms

Published online by Cambridge University Press:  20 November 2018

Zhi-Ming Ma  and
Michael Röckner
Zhi-Ming Ma
Affiliation:
Institute of Applied Mathematics, Academia Sinica, Beijng, China
Michael Röckner
Affiliation:
Fakultät für Mathematik, Universittät Bielefeld,Postfach 100131, D-33501 Bielefeld, Germany
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Abstract

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Coercive closed forms on L2-spaces are studied whose associated L2-semigroups are positivity preserving. Earlier work by other authors is extended by further developing the potential theory of such forms and completed by proving an analytic characterization of those of these forms which have a probabilistic counterpart, i.e., are associated with (special standard) Markov processes. Examples with finite and infinite dimensional state spaces are discussed.

Keywords

31C2560J4060J4531C15positivity preserving coercive formsDirichlet formsquasi-regularitycapacitiesMarkov processes
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 47 , Issue 4 , 01 August 1995 , pp. 817 - 840
Copyright
Copyright © Canadian Mathematical Society 1995

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