Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

Article

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J. Korean Math. Soc. 2016; 53(1): 57-72

Printed January 1, 2016

https://doi.org/10.4134/JKMS.2016.53.1.57

Copyright © The Korean Mathematical Society.

Maximal inequalities and an application under a weak dependence

Eunju Hwang and Dong Wan Shin

Gachon University, Ewha University

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--342], 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.

Keywords: weak dependence, maximal moment inequality, linear process, functional central limit theorem

MSC numbers: Primary 60E15, 60G99; Secondary 60F05