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.
Publié le : 2010-07-15
Classification:
Symmetric Markov process,
Dirichlet form,
Revuz measure,
martingale additive functionals of finite energy,
continuous additive functional of zero energy,
Nakao’s CAF of zero energy,
Fukushima decomposition,
semi-martingale,
Dirichlet processes,
stochastic integral,
Itô integral,
Fisk–Stratonovich integral,
time reversal operator,
dual predictable projection,
31C25,
60J25,
60J45,
60J75
@article{1278593959,
author = {Kuwae, Kazuhiro},
title = {Stochastic calculus over symmetric Markov processes without time reversal},
journal = {Ann. Probab.},
volume = {38},
number = {1},
year = {2010},
pages = { 1532-1569},
language = {en},
url = {http://dml.mathdoc.fr/item/1278593959}
}
Kuwae, Kazuhiro. Stochastic calculus over symmetric Markov processes without time reversal. Ann. Probab., Tome 38 (2010) no. 1, pp. 1532-1569. http://gdmltest.u-ga.fr/item/1278593959/