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A STRONG LAW OF LARGE NUMBERS FOR AANA RANDOM VARIABLES IN A HILBERT SPACE AND ITS APPLICATION

Ko, Mi-Hwa

  • Received : 2010.01.12
  • Accepted : 2010.02.22
  • Published : 2010.03.25

Abstract

In this paper we introduce the concept of asymptotically almost negatively associated random variables in a Hilbert space and obtain the strong law of large numbers for a strictly stationary asymptotically almost negatively associated sequence of H-valued random variables with zero means and finite second moments. As an application we prove a strong law of large numbers for a linear process generated by asymptotically almost negatively random variables in a Hilbert space with this result.

Keywords

Almost sure convergence;linear process in a Hilbert space;asymptotically almost negatively associated;linear operator;Hilbert space valued random variable

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