Convergence rates in the law of large numbers. II
1968 ◽
Vol 64
(2)
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pp. 485-488
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Keyword(s):
Let {Xn: n ≥ 1} be a sequence of independent random variables and write Suppose that the random vairables Xn are uniformly bounded by a random variable X in the sense thatSet qn(x) = Pr(|Xn| > x) and q(x) = Pr(|Xn| > x). If qn ≤ q and E|X|r < ∞ with 0 < r < 2 then we have (see Loève(4), 242)where ak = 0, if 0 < r < 1, and = EXk if 1 ≤ r < 2 and ‘a.s.’ stands for almost sure convergence. the purpose of this paper is to study the rates of convergence ofto zero for arbitrary ε > 0. We shall extend to the present context, results of (3) where the case of identically distributed random variables was treated. The techniques used here are strongly related to those of (3).
1971 ◽
Vol 8
(01)
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pp. 52-59
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2012 ◽
Vol 05
(01)
◽
pp. 1250007
1987 ◽
Vol 10
(4)
◽
pp. 805-814
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2016 ◽
Vol 32
(1)
◽
pp. 58-66
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Keyword(s):
1969 ◽
Vol 141
◽
pp. 443-443
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Keyword(s):
1966 ◽
Vol 72
(2)
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pp. 266-269
◽
Keyword(s):
2000 ◽
Vol 13
(3)
◽
pp. 261-267
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