Stochastic Calculus for Markov Processes Associated with Non-symmetric Dirichlet Forms

TL;DR

This paper extends Nakao's stochastic integrals and Ito's formula to non-symmetric Dirichlet forms, broadening the mathematical tools available for analyzing Markov processes with non-symmetric characteristics.

Contribution

It introduces an extension of stochastic integrals and Ito's formula from symmetric to non-symmetric Dirichlet forms, enhancing the theoretical framework for Markov processes.

Findings

Extended Nakao's stochastic integrals to non-symmetric forms

Derived Ito's formula in the non-symmetric setting

Provided mathematical tools for analyzing non-symmetric Markov processes

Abstract

Nakao's stochastic integrals for continuous additive functionals of zero energy are extended from the symmetric Dirichlet forms setting to the non-symmetric Dirichlet forms setting. Ito's formula in terms of the extended stochastic integrals is obtained.