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Let ${{\xi}_k,k{\in}{\mathbb{Z}}}$ be an associated H-valued random variables with $E{\xi}_k$ = 0, $E{\parallel}{\xi}_k{\parallel}$ < ${\infty}$ and $E{\parallel}{\xi}_k{\parallel}^2$ < ${\infty}$ and {$a_k,k{\in}{\mathbb{Z}}$} a sequence of bounded linear operators such that ${\sum}^{\infty}_{j=0}j{\parallel}a_j{\parallel}_{L(H)}$ < ${\infty}$. We define the sationary Hilbert space process $X_k={\sum}^{\infty}_{j=0}a_j{\xi}_{k-j}$ and prove that $n^{-1}{\sum}^n_{k=1}X_k$ converges to zero.
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참고문헌 (9)
참고문헌 신청
Araujo, A / 1980 / The Central Limit Theorem for Real and Banach Valued Random Variables / John Wiley and Sons.
Birkel, T / 1989 / A note on the strong law of large numbers for positively dependent random variables / Statist. Probab. Lett 7:17~20
Brockwell, P / 1987 / Time series, Theory and Method / Springer
Burton, R / 1986 / An invariance principle for weakly associated random vectors / Stochastic Processes Appl 23:301~306
Esary, J. / 1967 / Association of random variables with applications / Ann. Math. Statist 38:1466~1474
Birkel, T / 1989 / A note on the strong law of large numbers for positively dependent random variables / Statist. Probab. Lett 7:17~20
Brockwell, P / 1987 / Time series, Theory and Method / Springer
Burton, R / 1986 / An invariance principle for weakly associated random vectors / Stochastic Processes Appl 23:301~306
Esary, J. / 1967 / Association of random variables with applications / Ann. Math. Statist 38:1466~1474
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