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On the Weak Limiting Behavior of Almost Surely Convergent Row Sums from Infinite Arrays of Rowwise Independent Random Elements in Banach Spaces |
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| Authors: | A Rosalsky A I Volodin |
| Institution: | (1) Department of Statistics, University of Florida, Gainesville, Florida, 32611;(2) Department of Mathematics, University of Regina, Regina, Saskatchewan, Canada, S4S 0A2 |
| Abstract: | For an array {V
nk
,k 1,n1} of rowwise independent random elements in a real separable Banach space
with almost surely convergent row sums
, we provide criteria for S
n
–A
n
to be stochastically bounded or for the weak law of large numbers
to hold where {A
n
,n1} is a (nonrandom) sequence in
. |
| Keywords: | Real separable Banach space infinite array of rowwise independent random elements almost surely convergent row sums infinitesimal array |
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