Open Access
May 2008 Stochastic calculus for symmetric Markov processes
Z.-Q. Chen, P. J. Fitzsimmons, K. Kuwae, T.-S. Zhang
Ann. Probab. 36(3): 931-970 (May 2008). DOI: 10.1214/07-AOP347

Abstract

Using time-reversal, we introduce a stochastic integral for zero-energy additive functionals of symmetric Markov processes, extending earlier work of S. Nakao. Various properties of such stochastic integrals are discussed and an Itô formula for Dirichlet processes is obtained.

Citation

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Z.-Q. Chen. P. J. Fitzsimmons. K. Kuwae. T.-S. Zhang. "Stochastic calculus for symmetric Markov processes." Ann. Probab. 36 (3) 931 - 970, May 2008. https://doi.org/10.1214/07-AOP347

Information

Published: May 2008
First available in Project Euclid: 9 April 2008

zbMATH: 1142.31005
MathSciNet: MR2408579
Digital Object Identifier: 10.1214/07-AOP347

Subjects:
Primary: 31C25
Secondary: 60H05 , 60J55 , 60J57

Keywords: additive functional , dual additive functional , dual predictable projection , generalized Itô formula , martingale additive functional , Revuz measure , stochastic integral , symmetric Markov process , Time reversal

Rights: Copyright © 2008 Institute of Mathematical Statistics

Vol.36 • No. 3 • May 2008
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