ON ALMOST SURE CONVERGENCE OF WEIGHTED SUMS OF RANDOM ELEMENT SEQUENCES

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

Abstract

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

CLC Number:

60B11

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.

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