Relative stability and the strong law of large numbers |
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| Authors: | R. A. Maller |
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| Affiliation: | (1) Division of Mathematics & Statistics, Australian National University and C.S.I.R.O., South Melbourne, Vic, Australia |
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| Abstract: | Summary LetX1,X2,..., be i.i.d. random variables andSn=X1+X2+ . +Xn. In this paper we simplify Rogozin's condition forSn/Bn ±1for someBn + , which generalises Hin in's condition for relative stability ofSn. We also consider convergence of subsequences ofSn/Bn. As an application of our methods, we extend a result of Chow and Robbins to show thatSn/Bn±1 a.s. for someBn + if and only if 0<¦EX¦ E¦X¦<+ . |
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