Acta mathematica scientia, Series B >
ON ALMOST SURE CONVERGENCE OF WEIGHTED SUMS OF RANDOM ELEMENT SEQUENCES
Received date: 2007-03-14
Revised date: 2008-05-20
Online published: 2010-07-20
Supported by
Supported by the National Natural Science Foundation of China (10671149)
We mainly study the almost sure limiting behavior of weighted sums of the form ∑ni=1ai Xi / 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.
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 . DOI: 10.1016/S0252-9602(10)60099-9
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