Tohoku Mathematical Journal
2018

March
SECOND SERIES VOL. 70, NO. 1

Tohoku Math. J.
70 (2018), 97-119

Title STOCHASTIC CALCULUS FOR MARKOV PROCESSES ASSOCIATED WITH SEMI-DIRICHLET FORMS

Author Chuan-Zhong Chen, Li Ma and Wei Sun

(Received December 17, 2014, revised November 27, 2015)
Abstract. We present a new Fukushima type decomposition in the framework of semi-Dirichlet forms. This generalizes the result of Ma, Sun and Wang [17, Theorem 1.4] by removing the condition (S). We also extend Nakao's integral to semi-Dirichlet forms and derive Itô's formula related to it.

Mathematics Subject Classification. Primary 31C25; Secondary 60J25.

Key words and phrases. Semi-Dirichlet form, Fukushima type decomposition, zero quadratic variation process, Nakao's integral, Itô's formula.

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