A new weak dependence condition and applications to moment inequalities

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:84

Article

Doukhan, P ; Louhichi, S

关键词: stationary sequences;    inequalities;    Rosenthal inequality;    positive dependence;    mixing;    central limit theorem;   

DOI  :  10.1016/S0304-4149(99)00055-1

来源: Elsevier

【 摘 要 】

The purpose of this paper is to propose a unifying weak dependence condition. Mixing sequences, functions of associated or Gaussian sequences, Bernoulli shifts as well as models with a Markovian representation are examples of the models considered. We establish Marcinkiewicz-Zygmund, Rosenthal and exponential inequalities for general sequences of centered random variables. Inequalities are stated in terms of the decay rate for the covariance of products of the initial random variables subject to the condition that the gap of time between both products tends to infinity. As applications of those notions, we obtain a version of the functional CLT and an invariance principle for the empirical process (C) 1999 Elsevier Science B.V. All rights reserved. MSG: 60E15; 60F05; 60F17; 60G10; 60G99.

【 授权许可】

Free