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
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
This paper investigates some conditions which imply the strong laws of large numbers for Bana ch space val-ued random variable sequences.Some generalizations of the Marcinkiewicz-Zygmund theorem and the Hoffmann-Jdprg...This paper investigates some conditions which imply the strong laws of large numbers for Bana ch space val-ued random variable sequences.Some generalizations of the Marcinkiewicz-Zygmund theorem and the Hoffmann-Jdprgensen and Pisier theorem are obtained.展开更多
Let {β（n）}n be a sequence of positive numbers such that β（0） = 1 and let 1 ≤ p 〈 ≤. We will investigate the reflexivity of all integer powers of the multiplication operator on the Banach spaces of formal Laur...Let {β（n）}n be a sequence of positive numbers such that β（0） = 1 and let 1 ≤ p 〈 ≤. We will investigate the reflexivity of all integer powers of the multiplication operator on the Banach spaces of formal Laurent series, L^P（β）.展开更多
基金Supported by the National Natural Science Foundationof China (10671149)
文摘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.
基金supported in part by the National Foundation for Science Technology Development,Vietnam (NAFOSTED) (Grant No. 101.02.32.09)
文摘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.
基金Supported by the National Natrual Science Foun dation of ChiYla(10071058)
文摘This paper investigates some conditions which imply the strong laws of large numbers for Bana ch space val-ued random variable sequences.Some generalizations of the Marcinkiewicz-Zygmund theorem and the Hoffmann-Jdprgensen and Pisier theorem are obtained.
文摘Let {β（n）}n be a sequence of positive numbers such that β（0） = 1 and let 1 ≤ p 〈 ≤. We will investigate the reflexivity of all integer powers of the multiplication operator on the Banach spaces of formal Laurent series, L^P（β）.
