STRONG LAWS OF LARGE NUMBERS FOR LINEAR PROCESSES GENERATED BY ASSOCIATED RANDOM VARIABLES IN A HILBERT SPACE

• Journal title : Honam Mathematical Journal
• Volume 30, Issue 4,  2008, pp.703-711
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2008.30.4.703
Title & Authors
STRONG LAWS OF LARGE NUMBERS FOR LINEAR PROCESSES GENERATED BY ASSOCIATED RANDOM VARIABLES IN A HILBERT SPACE
Ko, Mi-Hwa;

Abstract
Let $\small{{{\xi}_k,k{\in}{\mathbb{Z}}}}$ be an associated H-valued random variables with $\small{E{\xi}_k}$ = 0, $\small{E{\parallel}{\xi}_k{\parallel}}$ < $\small{{\infty}}$ and $\small{E{\parallel}{\xi}_k{\parallel}^2}$ < $\small{{\infty}}$ and {$\small{a_k,k{\in}{\mathbb{Z}}}$} a sequence of bounded linear operators such that $\small{{\sum}^{\infty}_{j=0}j{\parallel}a_j{\parallel}_{L(H)}}$ < $\small{{\infty}}$. We define the sationary Hilbert space process $\small{X_k={\sum}^{\infty}_{j=0}a_j{\xi}_{k-j}}$ and prove that $\small{n^{-1}{\sum}^n_{k=1}X_k}$ converges to zero.
Keywords
Strong laws of large numbers;linear process;associated;linear operator;H-valued random variable;
Language
English
Cited by
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