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

Journal of Mathematical Sciences

Liu, Jingjun¹  Liang, Song¹ 

关键词: Laplace Approximations;    Large Deviations;    Markov Chain;   

DOI  :  

学科分类：数学（综合）

来源: University of Tokyo * Department of Mathematical Sciences

【 摘 要 】

Let$L_n$betheempiricalmeasureofauniformlyergodicnonreversibleMarkovchainonacompactmetricspaceand$Φ$beasmoothfunctional.Thispapergivesapreciseasymptoticevaluationoftheform$E(exp(nΦ(L_n)))$uptoorder$1+o(1)$,inthecasetheHessianof$J-Φ$isnondegenerate,where$J$istheratefunctionofthelargedeviationsofempiricalmeasure.

【 授权许可】

Unknown