## Tohoku Mathematical Journal

- Tohoku Math. J. (2)
- Volume 70, Number 4 (2018), 633-648.

### Large deviations for continuous additive functionals of symmetric Markov processes

#### Abstract

Let $X$ be a locally compact separable metric space and $m$ a positive Radon measure on $X$ with full topological support. Let ${\bf{M}}=(P_x,X_t)$ be an $m$-symmetric Markov process on $X$. Let $(\mathcal{E},\mathcal{D}(\mathcal{E}))$ be the Dirichlet form on $L^2(X;m)$ generated by ${\bf{M}}$. Let $\mu$ be a positive Radon measure in the *Green-tight Kato class* and $A^\mu_t$ the positive continuous additive functional in the Revuz correspondence to $\mu$. Under certain conditions, we establish the large deviation principle for positive continuous additive functionals $A^\mu_t$ of symmetric Markov processes.

#### Article information

**Source**

Tohoku Math. J. (2), Volume 70, Number 4 (2018), 633-648.

**Dates**

First available in Project Euclid: 4 January 2019

**Permanent link to this document**

https://projecteuclid.org/euclid.tmj/1546570828

**Digital Object Identifier**

doi:10.2748/tmj/1546570828

**Mathematical Reviews number (MathSciNet)**

MR3896140

**Zentralblatt MATH identifier**

07040979

**Subjects**

Primary: 31C25: Dirichlet spaces

Secondary: 31C05: Harmonic, subharmonic, superharmonic functions 60J25: Continuous-time Markov processes on general state spaces

**Keywords**

large deviation continuous additive functional Dirichlet form symmetric Markov process

#### Citation

Yang, Seunghwan. Large deviations for continuous additive functionals of symmetric Markov processes. Tohoku Math. J. (2) 70 (2018), no. 4, 633--648. doi:10.2748/tmj/1546570828. https://projecteuclid.org/euclid.tmj/1546570828