On convergence rates and the expectation of sums of random variables |
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Authors: | R.A. Maller |
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Affiliation: | CSIRO Division of Mathematics & Statistics, P.O. Box 310, South Melbourne, Vic. 3205, Australia |
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Abstract: | Let Xi be iidrv's and Sn=X1+X2+…+Xn. When EX21<+∞, by the law of the iterated logarithm for some constants αn. Thus the r.v. is a.s.finite when δ>0. We prove a rate of convergence theorem related to the classical results of Baum and Katz, and apply it to show, without the prior assumption EX21<+∞ that EYh<+∞ if and only if for 0<h<1 and δ> , whereas whenever h>0 and . |
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Keywords: | Convergence rates optimal stopping law of the iterated logarithm |
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