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Convergence of double series of random elements in Banach spaces

Nguyen Duy Tien|Le Van Dung
대한수학회 (The Korean Mathematical Society)|2012.09|대한수학회지 (Journal of the KMS)|제49권 제5호|pp. 1053-1064

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참고문헌

키워드

strong laws of large numbersp-uniformly smooth Banach spacesconvergence of double random seriesdouble array of random elements.
주제분류수학

초록

For a double array of random elements {Xmn;m ≥ 1, n ≥ 1} in a p-uniformly smooth Banach space, {bmn;m ≥ 1, n ≥1} is an array of positive numbers, convergence of double random series Σ1수식mnXmn and strong law of large numbers 수식are established.

Abstract

For a double array of random elements {Xmn;m ≥ 1, n ≥ 1} in a p-uniformly smooth Banach space, {bmn;m ≥ 1, n ≥1} is an array of positive numbers, convergence of double random series Σ1수식mnXmn and strong law of large numbers 수식are established.

참고문헌 (14)

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  9. A. Rosalsky, "Strong and weak laws of large numbers for double sums of independent random elements in Rademacher type p Banach spaces", Stoch. Anal. Appl, 24(6), pp.1097~1117 (2006)
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관련 논문AI추천

MEAN CONVERGENCE THEOREMS AND WEAK LAWS OF LARGE NUMBERS FOR DOUBLE ARRAYS OF RANDOM ELEMENTS IN BANACH SPACESLe Van Dung, Nguyen Duy Tien대한수학회 · 대한수학회보2010 · 제47권 제3호COMPLETE CONVERGENCE FOR WEIGHTED SUMS OF RANDOM ELEMENTS성수학대한수학회 · 대한수학회보2010 · 제47권 제2호On the weak laws with random indices for partial sums for arrays of random elements in martingale type $p$ Banach spaces성수학, Andrei I. Volodin, Tien-Chung Hu대한수학회 · 대한수학회보2006 · 제43권 제3호On the weal law of large numbers for sequences of Banach space valued random elementsLe hong Son, Nguyen Van Quang대한수학회 · 대한수학회보2006 · 제43권 제3호ON THE CONVERGENCE OF SERIES OF MARTINGALE DIFFERENCES WITH MULTIDIMENSIONAL INDICESDang Hung Thang, Ta Cong Son대한수학회 · 대한수학회지2015 · 제52권 제5호Weak laws of large numbers for arrays under a condition of uniform integrability성수학, Andrei Volodin, Supranee Lisawadi대한수학회 · 대한수학회지2008 · 제45권 제1호

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