Stochastic Calculus for Markov Processes Associated with Non-symmetric   Dirichlet Forms
  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. 
Chuan-Zhong Chen, Li Ma, Wei Sun
math.PR