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Zbl 1035.60021
Chen, Xia; Guillin, Arnaud
The functional moderate deviations for Harris recurrent Markov chains and applications. (English)
[J] Ann. Inst. Henri Poincaré, Probab. Stat. 40, No. 1, 89-124 (2004). ISSN 0246-0203

The authors study exponentially asymptotic behaviors for the trajectories of additive functionals of Harris Markov chains. In the main result, the authors establish a moderate deviation principle for a pair of additive functionals of different growth rates. Explicit formulas for the rate functions which exhibit a non-quadratic behavior are also given. In particular, the authors achieve the functional moderate deviations in two different scales. As an application, a functional law of LIL is presented, which leads to a variety of strong limit laws in the spirit of Strassen.
[Zdzislaw Rychlik (Lublin)]

MSC 2000:: *60F10 Large deviations
60F15 Strong limit theorems
60F17 Functional limit theorems
60J55 Additive functionals

Keywords: Harris recurent Markov chain; p-regualarity; moderate deviation; the law of the iterated logarithm

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