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July 2010 Stochastic calculus over symmetric Markov processes without time reversal
Kazuhiro Kuwae
Ann. Probab. 38(4): 1532-1569 (July 2010). DOI: 10.1214/09-AOP516


We refine stochastic calculus for symmetric Markov processes without using time reverse operators. Under some conditions on the jump functions of locally square integrable martingale additive functionals, we extend Nakao’s divergence-like continuous additive functional of zero energy and the stochastic integral with respect to it under the law for quasi-everywhere starting points, which are refinements of the previous results under the law for almost everywhere starting points. This refinement of stochastic calculus enables us to establish a generalized Fukushima decomposition for a certain class of functions locally in the domain of Dirichlet form and a generalized Itô formula.


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Kazuhiro Kuwae. "Stochastic calculus over symmetric Markov processes without time reversal." Ann. Probab. 38 (4) 1532 - 1569, July 2010.


Published: July 2010
First available in Project Euclid: 8 July 2010

zbMATH: 1206.31009
MathSciNet: MR2663636
Digital Object Identifier: 10.1214/09-AOP516

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

Keywords: continuous additive functional of zero energy , Dirichlet form , Dirichlet processes , dual predictable projection , Fisk–Stratonovich integral , Fukushima decomposition , Itô integral , martingale additive functionals of finite energy , Nakao’s CAF of zero energy , Revuz measure , semi-martingale , stochastic integral , symmetric Markov process , time reversal operator

Rights: Copyright © 2010 Institute of Mathematical Statistics


Vol.38 • No. 4 • July 2010
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