Tail sums of convergent series of independent random variables
1974 ◽
Vol 75
(3)
◽
pp. 361-364
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Keyword(s):
Let X1, X2, … be a sequence of independent random variables such that, for each n ≥ 1, EXn = 0 and and assume that then converges almost surely as N → ∞. Let and let Fn(x) denote the distribution function of Xn. Loynes (2) observed that the sequence {Sn} is a reversed martingale, and applied his central limit theorem to it: however, stronger results are obtainable, in precise duality with the classical theory of partial sums of independent random variables. These results describe the fluctuations of the sequence {Sn}, and hence the way in which converges to its limit.
1994 ◽
Vol 17
(2)
◽
pp. 323-340
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Keyword(s):
1969 ◽
Vol 10
(1-2)
◽
pp. 219-230
1990 ◽
Vol 145
(1)
◽
pp. 345-364
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2017 ◽
Vol 57
(2)
◽
pp. 244-258
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Keyword(s):
1994 ◽
Vol 26
(01)
◽
pp. 104-121
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1985 ◽
pp. 144-179
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1963 ◽
Vol 11
(1-2)
◽
pp. 97-102
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