On the order of growth of convergent series of independent random variables
2004 ◽
Vol 2004
(2)
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pp. 159-168
Keyword(s):
For independent random variables, the order of growth of the convergent series Sn is studied in this paper. More specifically, if the series Sn converges almost surely to a random variable, the tail series is a well-defined sequence of random variables and converges to 0 almost surely. For the almost surely convergent series Sn, a tail series strong law of large numbers (SLLN) is constructed by investigating the duality between the limiting behavior of partial sums and that of tail series.
2013 ◽
Vol 2013
◽
pp. 1-7
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2016 ◽
Vol 32
(1)
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pp. 58-66
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2012 ◽
Vol 05
(01)
◽
pp. 1250007
1999 ◽
Vol 22
(1)
◽
pp. 171-177
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1997 ◽
Vol 86
(5-6)
◽
pp. 1373-1384
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Keyword(s):
2010 ◽
Vol 47
(04)
◽
pp. 908-922
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2010 ◽
Vol 43
(4)
◽
pp. 217-219
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Keyword(s):
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