Fukushima type decomposition for semi-Dirichlet forms
  We present a Fukushima type decomposition in the setting of general quasi-regular semi-Dirichlet forms. The decomposition is then employed to give a transformation formula for martingale additive functionals. Applications of the results to some concrete examples of semi-Dirichlet forms are given at the end of the paper. We discuss also the uniqueness question about Doob-Meyer decomposition on optional sets of interval type. 
Zhi-Ming Ma, Wei Sun and Li-Fei Wang
math.PR