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MAXIMAL INEQUALITIES AND AN APPLICATION UNDER A WEAK DEPENDENCE

  • Received : 2014.06.30
  • Published : 2016.01.01

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

Acknowledgement

Supported by : National Research Foundation of Korea (NRF)

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