MAXIMAL INEQUALITIES AND AN APPLICATION UNDER A WEAK DEPENDENCE

Abstract

We establish maximal moment inequalities of partial sums under psi-weak dependence, which has been proposed by Doukhan and Louhichi [P. Doukhan and S. Louhichi, A new weak dependence condition and application to moment inequality, Stochastic Process. Appl. 84 (1999), 313-3421, to unify weak dependence such as mixing, association, Gaussian sequences and Bernoulli shifts. As an application of maximal moment inequalities, a functional central limit theorem is developed for linear processes with psi-weakly dependent innovations.