ON ALMOST SURE CONVERGENCE OF WEIGHTED SUMS OF RANDOM ELEMENT SEQUENCES

doi:10.1016/S0252-9602(10)60099-9

数学物理学报(英文版) ›› 2010, Vol. 30 ›› Issue (4): 1021-1028.doi: 10.1016/S0252-9602(10)60099-9

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ON ALMOST SURE CONVERGENCE OF WEIGHTED SUMS OF RANDOM ELEMENT SEQUENCES

甘师信

School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China

收稿日期:2007-03-14 修回日期:2008-05-20 出版日期:2010-07-20 发布日期:2010-07-20
基金资助:
Supported by the National Natural Science Foundation of China (10671149)

ON ALMOST SURE CONVERGENCE OF WEIGHTED SUMS OF RANDOM ELEMENT SEQUENCES

GAN Shi-xin

School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China

Received:2007-03-14 Revised:2008-05-20 Online:2010-07-20 Published:2010-07-20
Supported by:
Supported by the National Natural Science Foundation of China (10671149)

摘要/Abstract

摘要：

We mainly study the almost sure limiting behavior of weighted sums of the form ∑ⁿ_i₌₁a_iX_i/ _bn, where {X_n, n ≥ 1} is an arbitrary Banach space valued random element sequence or Banach space valued martingale difference sequence and {a_n, n ≥ 1} and {b_n, n ≥ 1} are two sequences of positive constants. Some new strong laws of large numbers for such weighted sums are proved under mild conditions.

关键词: Strong law of large number, almost sure convergence, L^pconvergence, weighted sums, Banach space valued
random element sequence, Banach space martingale difference sequence

Abstract:

We mainly study the almost sure limiting behavior of weighted sums of the form ∑ⁿ_i₌₁a_iX_i/ b_n, where {X_n, n ≥ 1} is an arbitrary Banach space valued random element sequence or Banach space valued martingale difference sequence and {a_n, n ≥ 1} and {b_n, n ≥ 1} are two sequences of positive constants. Some new strong laws of large numbers for such weighted sums are proved under mild conditions.

Key words: Strong law of large number, almost sure convergence, L^pconvergence, weighted sums, Banach space valued
random element sequence, Banach space martingale difference sequence

中图分类号:

60B11

甘师信. ON ALMOST SURE CONVERGENCE OF WEIGHTED SUMS OF RANDOM ELEMENT SEQUENCES[J]. 数学物理学报(英文版), 2010, 30(4): 1021-1028.

GAN Shi-xin. ON ALMOST SURE CONVERGENCE OF WEIGHTED SUMS OF RANDOM ELEMENT SEQUENCES[J]. Acta mathematica scientia,Series B, 2010, 30(4): 1021-1028.

参考文献

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[14] Nguyen Dug Tien, Nguyen Van Hung. On convergence of weighted sums of martingale ifferences//Probability Theory on Vector Spaces IV. Springer's LNM, 1987

ON ALMOST SURE CONVERGENCE OF WEIGHTED SUMS OF RANDOM ELEMENT SEQUENCES

ON ALMOST SURE CONVERGENCE OF WEIGHTED SUMS OF RANDOM ELEMENT SEQUENCES

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