## Tohoku Mathematical Journal

### Fukushima type decomposition for semi-Dirichlet forms

#### 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.

#### Article information

Source
Tohoku Math. J. (2), Volume 68, Number 1 (2016), 1-27.

Dates
First available in Project Euclid: 17 March 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1458248859

Digital Object Identifier
doi:10.2748/tmj/1458248859

Mathematical Reviews number (MathSciNet)
MR3476133

Zentralblatt MATH identifier
1343.31007

Subjects
Primary: 31C25: Dirichlet spaces
Secondary: 60J25: Continuous-time Markov processes on general state spaces

#### Citation

Ma, Zhi-Ming; Sun, Wei; Wang, Li-Fei. Fukushima type decomposition for semi-Dirichlet forms. Tohoku Math. J. (2) 68 (2016), no. 1, 1--27. doi:10.2748/tmj/1458248859. https://projecteuclid.org/euclid.tmj/1458248859

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