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On the limiting behavior of randomly weighted partial sums

✍ Scribed by Andrew Rosalsky; M. Sreehari

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
413 KB
Volume
40
Category
Article
ISSN
0167-7152

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✦ Synopsis

We study the almost sure limiting behavior and convergence in probability of weighted partial sums of the form ~-~j=l, W~jX, j where { W~j, 1 -.~j ~< n, n 1> 1 } and {X,j, 1 ~~ 1 }are triangular arrays of random variables. The results obtain irrespective of the joint distributions of the random variables within each array. Applications concerning the Efron bootstrap and queueing theory are discussed.

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## Abstract Let {__S~n~__, __n__ β‰₯ 1} be partial sums of independent identically distributed random variables. The almost sure version of CLT is generalized on the case of randomly indexed sums {__S~Nn~__, __n__ β‰₯ 1}, where {__N~n~__, __n__ β‰₯ 1} is a sequence of positive integer‐valued random varia