## On the Precise Laplace Approximation for Large Deviations of Markov Chain The Nondegenerate Case

J. Math. Sci. Univ. Tokyo
Vol. 10 (2003), No. 2, Page 421--454.

Liang, Song ; Liu, Jingjun
On the Precise Laplace Approximation for Large Deviations of Markov Chain The Nondegenerate Case
Let $L_n$ be the empirical measure of a uniformly ergodic nonreversible Markov chain on a compact metric space and $Î¦$ be a smooth functional. This paper gives a precise asymptotic evaluation of the form $E(\exp(nÎ¦(L_n)))$ up to order $1+o(1)$, in the case the Hessian of $J-Î¦$ is nondegenerate, where $J$ is the rate function of the large deviations of empirical measure.