Some Strong Laws of Large Numbers for Blockwise Martingale Difference Sequences in Martingale Type p Banach Spaces  

作　　者：Andrew ROSALSKY Le Van THANH 

机构地区：[1]Department of Statistics,University of Florida [2]Department of Mathematics,Vinh University

出　　处：《Acta Mathematica Sinica,English Series》2012年第7期1385-1400,共16页数学学报（英文版）

基　　金：supported in part by the National Foundation for Science Technology Development,Vietnam (NAFOSTED) (Grant No. 101.02.32.09)

摘　　要：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.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.

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 

分 类 号：O177.2[理学—数学] O211.4[理学—基础数学]