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ON ALMOST SURE CONVERGENCE OF WEIGHTED SUMS OF RANDOM ELEMENT SEQUENCES
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作者 甘师信 《Acta Mathematica Scientia》 SCIE CSCD 2010年第4期1021-1028,共8页
We mainly study the almost sure limiting behavior of weighted sums of the form ∑ni=1 aiXi/bn , where {Xn, n ≥ 1} is an arbitrary Banach space valued random element sequence or Banach space valued martingale differen... We mainly study the almost sure limiting behavior of weighted sums of the form ∑ni=1 aiXi/bn , where {Xn, n ≥ 1} is an arbitrary Banach space valued random element sequence or Banach space valued martingale difference sequence and {an, n ≥ 1} and {bn,n ≥ 1} are two sequences of positive constants. Some new strong laws of large numbers for such weighted sums are proved under mild conditions. 展开更多
关键词 Strong law of large number almost sure convergence Lp convergence weighted sums banach space valued random element sequence banach space martingale difference sequence
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Some Strong Laws of Large Numbers for Blockwise Martingale Difference Sequences in Martingale Type p Banach Spaces 被引量:1
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作者 Andrew ROSALSKY Le Van THANH 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2012年第7期1385-1400,共16页
For a blockwise martingale difference sequence of random elements {Vn, n ≥ 1} taking values in a real separable martingale type p (1 ≤ p ≤ 2) Banach space, conditions are provided for strong laws of large numbers... For a blockwise martingale difference sequence of random elements {Vn, n ≥ 1} taking values in a real separable martingale type p (1 ≤ p ≤ 2) Banach space, conditions are provided for strong laws of large numbers of the form limn→∞ Vi/gn = 0 almost surely to hold where the constants gn ↑∞. A result of Hall and Heyde [Martingale Limit Theory and Its Application, Academic Press, New York, 1980, p. 36] which was obtained for sequences of random variables is extended to a martingale type p (1〈 p ≤2) Banach space setting and to hold with a Marcinkiewicz-Zygmund type normalization. Illustrative examples and counterexamples are provided. 展开更多
关键词 sequence of banach space valued random elements blockwise martingale difference sequence strong law of large numbers almost sure convergence martingale type p banach space
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On the Strong Law of Large Numbers for Non-Independent B-Valued Random Variables
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作者 GanShi-xin 《Wuhan University Journal of Natural Sciences》 EI CAS 2004年第1期13-17,共5页
This paper investigates some conditions which imply the strong laws of large numbers for Banach space valued random variable sequences. Some generalizations of the Marcinkiewicz-Zygmund theorem and the Hoffmann-J?rgen... This paper investigates some conditions which imply the strong laws of large numbers for Banach space valued random variable sequences. Some generalizations of the Marcinkiewicz-Zygmund theorem and the Hoffmann-J?rgensen and Pisier theorem are obtained. Key words strong law of large numbers - Banach space valued random variable sequence - p-smoothable Banach space CLC number O 211.4 - O 211.6 Foundation item: Supported by the National Natural Science Foundation of China (10071058)Biography: Gan Shi-xin (1939-), male, Professor, research direction: martingale theory, probability limiting theory and Banach space geometry theory. 展开更多
关键词 strong law of large numbers banach space valued random variable sequence p-smoothable banach space
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