Some variational formulas on additive functionals of symmetric Markov chains (Q2782644)

Donsker-Varadhan's type deviation of symmetric Markov processes with finite lifetime has been extended by \textit{M. Takeda} [Stochastics Stochastics Rep. 59, No. 1/2, 143-167 (1996; Zbl 0868.60018)] and he established the full large deviation principle. As a corollary, the variational formula on the lifetime was obtained represented by Dirichlet form generated by the Markov process. The authors treat the same problem for symmetric continuous time Markov chains. They obtain some formulas on total occupation times and limit theorems of additive functionals by using large deviation theory. The results are formulated as an application of the above-mentioned variational formula, with calculations of its exponential decay rates represented by Dirichlet forms.