## Tohoku Mathematical Journal

- Tohoku Math. J. (2)
- Volume 70, Number 1 (2018), 97-119.

### Stochastic calculus for Markov processes associated with semi-Dirichlet forms

Chuan-Zhong Chen, Li Ma, and Wei Sun

#### 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.

#### Article information

**Source**

Tohoku Math. J. (2), Volume 70, Number 1 (2018), 97-119.

**Dates**

First available in Project Euclid: 9 March 2018

**Permanent link to this document**

https://projecteuclid.org/euclid.tmj/1520564420

**Digital Object Identifier**

doi:10.2748/tmj/1520564420

**Mathematical Reviews number (MathSciNet)**

MR3772807

**Zentralblatt MATH identifier**

06873675

**Subjects**

Primary: 31C25: Dirichlet spaces

Secondary: 60J25: Continuous-time Markov processes on general state spaces

**Keywords**

semi-Dirichlet form Fukushima type decomposition zero quadratic variation process Nakao's integral Itô's formula

#### Citation

Chen, Chuan-Zhong; Ma, Li; Sun, Wei. Stochastic calculus for Markov processes associated with semi-Dirichlet forms. Tohoku Math. J. (2) 70 (2018), no. 1, 97--119. doi:10.2748/tmj/1520564420. https://projecteuclid.org/euclid.tmj/1520564420