Tohoku Mathematical Journal
2016
March
SECOND SERIES VOL. 68, NO. 1

Tohoku Math. J.
68 (2016), 1-27

Title FUKUSHIMA TYPE DECOMPOSITION FOR SEMI-DIRICHLET FORMS

Author Zhi-Ming Ma, Wei Sun and Li-Fei Wang

(Received February 17, 2014, revised August 6, 2014)
Abstract. 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.

Mathematics Subject Classification. Primary 31C25; Secondary 60J25.
Key words and phrases. Fukushima type decomposition, quasi-regular semi-Dirichlet forms, stochastic sets of interval type, transformation formula for martingale additive functionals.

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