On the Complete Convergence of Moving Average Process with Banach Space Valued Random Elements |
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Authors: | Tae-Sung Kim Mi-Hwa Ko |
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Institution: | (1) Department of Mathematics, WonKwang University, 570-749 Iksan, Republic of Korea |
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Abstract: | Let {Y
i
;−∞<i<∞} be a doubly infinite sequence of independent random elements taking values in a separable real Banach space and stochastically
dominated by a random variable X. Let {a
i
;−∞<i<∞} be an absolutely summable sequence of real numbers and set V
i
=∑
k=−∞∞
a
i+k
Y
i
,i≥1. In this paper, we derive that if
and E|X|
μ
log
ρ
|X|<0, for some μ (0<μ<2, μ≠1) and ρ>0 then
for all ε>0.
This work was partially supported by the Korean Research Foundation Grant funded by the Korean Government (KRF-2006-353-C00006,
KRF-2006-251-C00026). |
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Keywords: | Banach space valued random elements Complete convergence Rate of convergence Convergence in probability Moving average processes |
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