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
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Abstract:
Let $L_n$ be the empirical measure of a uniformly ergodic nonreversible Markov chain on a compact metric space and $Φ$ be a smooth functional. This paper gives a precise asymptotic evaluation of the form $E(\exp(nΦ(L_n)))$ up to order $1+o(1)$, in the case the Hessian of $J-Φ$ is nondegenerate, where $J$ is the rate function of the large deviations of empirical measure.

Keywords: Laplace Approximations, Large Deviations, Markov Chain

Mathematics Subject Classification (2000): 60F10, 60J15, 30J20
Mathematical Reviews Number: MR1987139

Received: 2001-11-30