Almost sure invariance principles via martingale approximation

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:122

Article

Merlevede, Florence²  Peligrad, Costel¹  Peligrad, Magda¹ 

[1] Univ Cincinnati, Dept Math Sci, Cincinnati, OH 45221 USA

[2] Univ Paris Est, Math Lab, CNRS, UMR 8050, F-77435 Champs Sur Marne, France

关键词: Martingale approximation;    Quenched CLT;    Almost sure CLT;    Normal Markov chains;    Functional CLT;    Law of the iterated logarithm;    Almost sure approximation;   

DOI  :  10.1016/j.spa.2011.09.004

来源: Elsevier

【 摘 要 】

In this paper, we estimate the rest of the approximation of a stationary process by a martingale in terms of the projections of partial sums. Then, based on this estimate, we obtain almost sure approximation of partial sums by a martingale with stationary differences. The results are exploited to further investigate the central limit theorem and its invariance principle started at a point, the almost sure central limit theorem, as well as the law of the iterated logarithm via almost sure approximation with a Brownian motion, improving the results available in the literature. The conditions are well suited for a variety of examples; they are easy to verify, for instance, for linear processes and functions of Bernoulli shifts. (C) 2011 Elsevier B.V. All rights reserved.

【 授权许可】

Free