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On the rate of complete convergence for weighted sums of arrays of random elements

성수학|Andrei I. Volodin
대한수학회 (The Korean Mathematical Society)|2006.07|대한수학회지 (Journal of the KMS)|제43권 제4호|pp. 815-828

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Abstract

Let {V_{nk}, k ge 1, nge 1} be an array of rowwise independent random elements which are stochasticallydominated by a random variable X with E|X|^{frac{alpha}{gamma}+theta}log^rho (|X|) <infty for somerho>0, alpha>0, gamma>0, theta>0 such that theta+alpha/gamma<2.Let {a_{nk}, k ge 1, nge 1} be an array of suitable constants.A complete convergence result is obtained for the weighted sums of the form sum_{k=1}^infty a_{nk}V_{nk}.

참고문헌 (11)

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  5. P. L. Hsu, "Complete convergence and the law of large numbers", 33, pp.25~ (1947)
  6. "On the rate of complete convergence for weighted sums of arrays of Banach space valued random elements", 47, pp.455~468 (2003)
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관련 논문AI추천

On complete convergence for arrays of rowwise independent random elements성수학, Manuel Ord\'o\~nez Cabrera, Tien-Chung Hu대한수학회 · 대한수학회지2007 · 제44권 제2호On the complete convergence for weighted sums of dependent random variables under condition of weighted integrabilityJong-Il Baek, Mi-Hwa Ko, Tae-Sung Kim대한수학회 · 대한수학회지2008 · 제45권 제4호On the weak law for weighted sums indexed by random variables under negatively associated arraysDong-Myong Lee, Jong-Il Baek대한수학회 · 대한수학회논문집2003 · 제18권 제1호On the almost sure convergence of weighted sums of negatively associated random variables박성태, 백종일, 서혜영, 정성모대한수학회 · 대한수학회논문집2005 · 제20권 제3호Convergence of weighted sums for dependent random variablesDong-Xia Zhang, Han-Ying Liang, Jong-Il Baek대한수학회 · 대한수학회지2004 · 제41권 제5호COMPLETE CONVERGENCE FOR WEIGHTED SUMS OF RANDOM ELEMENTS성수학대한수학회 · 대한수학회보2010 · 제47권 제2호

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