Tohoku Mathematical Journal
2018
December
SECOND SERIES VOL. 70, NO. 4

Tohoku Math. J.
70 (2018), 633-648

Title LARGE DEVIATIONS FOR CONTINUOUS ADDITIVE FUNCTIONALS OF SYMMETRIC MARKOV PROCESSES

Author Seunghwan Yang

(Received April 13, 2016, revised August 1, 2016)
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 {\it 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.

Mathematics Subject Classification. Primary 31C25; Secondary 31C05, 60J25.
Key words and phrases. Large deviation, continuous additive functional, Dirichlet form, symmetric Markov process.

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