The functional moderate deviations for Harris recurrent Markov chains and applications

被引：9

作者：

Chen, X

Guillin, A ^{[1
]}

机构：

[1] Univ Tennessee, Dept Math, Knoxville, TN 37996 USA

[2] Univ Paris 09, CEREMADE, F-75775 Paris 16, France

来源：

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES | 2004年 / 40卷 / 01期

基金：

美国国家科学基金会;

关键词：

Harris recurrent Markov chain; p-regularity; moderate deviation; the law of the iterated logarithm;

D O I：

10.1016/j.anihpb.2003.07.002

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We study exponentially asymptotic behaviors for the trajectories of additive functionals of Harris Markov chains. In the main result, we establish a moderate deviation principle for a pair of additive functionals of different growth rates. Moreover, we give explicit formulas for the rate functions which exhibit a non-quadratic behavior. In particular, we achieve the functional moderate deviations in two different scales. As an application, we obtain a functional law of LIL, which leads to a variety of strong limit laws in the spirit of Strassen [Z. Wahr. Geb. 3 (1964) 211-226]. (C) 2003 Elsevier SAS. All rights reserved.

引用

页码：89 / 124

页数：36

共 35 条

[1] NEW APPROACH TO THE LIMIT THEORY OF RECURRENT MARKOV-CHAINS [J].