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Stochastic calculus over symmetric Markov processes with time reversal

Published online by Cambridge University Press:  11 January 2016

K. Kuwae
K. Kuwae*
Affiliation:
Department of Mathematics and Engineering, Graduate School of Science and Technology, Kumamoto University, Kumamoto, 860-8555 Japan, kuwae@gpo.kumamoto-u.ac.jp
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Abstract

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We develop stochastic calculus for symmetric Markov processes in terms of time reversal operators. For this, we introduce the notion of the progressively additive functional in the strong sense with time-reversible defining sets. Most additive functionals can be regarded as such functionals. We obtain a refined formula between stochastic integrals by martingale additive functionals and those by Nakao's divergence-like continuous additive functionals of zero energy. As an application, we give a stochastic characterization of harmonic functions on a domain with respect to the infinitesimal generator of semigroup on L2-space obtained by lower-order perturbations.

Keywords

Primary 31C25Secondary 60J2560J4560J75
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 220 , December 2015 , pp. 91 - 148
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2015

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