Fukushima type decomposition for semi-Dirichlet forms (Q286714)

Fukushima's decomposition and the related transformation rules play the roles of the Doob-Meyer decomposition and Itô's formula in the framework of Dirichlet forms.NEWLINENEWLINEThe authors present a Fukushima-type decompostion for general quasi-regular semi-Dirichlet forms, apply the decomposition to give a transformation formula for martingale additive functionals, and give applications of the results to some concrete examples of semi-Dirichlet forms. In addition, the authors discuss the uniqueness question about the Doob-Meyer decomposition on optional sets of interval type.NEWLINENEWLINEThe main result of this paper (Theorem 1.4) extends the corresponding results in [\textit{L. Ma} et al., Stoch. Dyn. 12, No. 4, Paper No. 1250003, 31 p. (2012; Zbl 1255.60134)] and [\textit{Y. Oshima}, Semi-Dirichlet forms and Markov processes. Berlin: de Gruyter (2013; Zbl 1286.60002)].