Tohoku Mathematical Journal

Large deviations for continuous additive functionals of symmetric Markov processes

Seunghwan Yang

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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


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