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.
Eunju Hwang and Dong Wan Shin
Gachon University, Ewha University
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
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