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December 2015 Stochastic calculus over symmetric Markov processes with time reversal
K. Kuwae
Nagoya Math. J. 220(none): 91-148 (December 2015). DOI: 10.1215/00277630-3335905

Abstract

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.

Citation

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K. Kuwae. "Stochastic calculus over symmetric Markov processes with time reversal." Nagoya Math. J. 220 91 - 148, December 2015. https://doi.org/10.1215/00277630-3335905

Information

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

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

Rights: Copyright © 2015 Editorial Board, Nagoya Mathematical Journal

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Vol.220 • December 2015
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