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 the Doob-Meyer decomposition on optional sets of interval type.
"Fukushima type decomposition for semi-Dirichlet forms." Tohoku Math. J. (2) 68 (1) 1 - 27, 2016. https://doi.org/10.2748/tmj/1458248859