Open Access
December 2015 Stochastic calculus over symmetric Markov processes with time reversal
K. Kuwae
Nagoya Math. J. 220: 91-148 (December 2015). DOI: 10.1215/00277630-3335905


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.


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K. Kuwae. "Stochastic calculus over symmetric Markov processes with time reversal." Nagoya Math. J. 220 91 - 148, December 2015.


Received: 15 November 2012; Revised: 9 November 2013; Accepted: 18 February 2014; Published: December 2015
First available in Project Euclid: 1 December 2015

zbMATH: 1336.60104
MathSciNet: MR3429727
Digital Object Identifier: 10.1215/00277630-3335905

Primary: 31C25
Secondary: 60J25 , 60J45 , 60J75

Keywords: boundary value problem , continuous additive functional of zero energy , Dirichlet form , Dirichlet processes , dual predictable projection , Feynman-Kac transform , Fisk-Stratonovich integral , Fukushima decomposition , Girsanov transform , Itô integral , Lyons-Zheng decomposition , Markov process , martingale additive functionals of finite energy , Nakao’s CAF of zero energy , progressively additive functional , progressively additive functional in the strong sense , Revuz measure , Semimartingale , stochastic integral , time reversal operator

Rights: Copyright © 2015 Editorial Board, Nagoya Mathematical Journal

Vol.220 • December 2015
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