Stochastic integration with respect to additive functionals of zero quadratic variation

Abstract

We consider a Markov process $X$ associated to a nonnecessarily symmetric Dirichlet form $\mathcal{E}$. We define a stochastic integral with respect to a class of additive functionals of zero quadratic variation and then we obtain an Itô formula for the process $u(X)$, when $u$ is locally in the domain of $\mathcal{E}$.

Published in at http://dx.doi.org/10.3150/12-BEJ457 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)

References in corpus (3)

• Stochastic calculus for symmetric Markov processes
• On Itô's formula for elliptic diffusion processes
• Extended Itô calculus for symmetric Markov processes