Tohoku Mathematical Journal

Large deviations for continuous additive functionals of symmetric Markov processes

Seunghwan Yang

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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

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

First available in Project Euclid: 4 January 2019

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 31C25: Dirichlet spaces
Secondary: 31C05: Harmonic, subharmonic, superharmonic functions 60J25: Continuous-time Markov processes on general state spaces

large deviation continuous additive functional Dirichlet form symmetric Markov process


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.

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