On the strong law of large numbers for dependent random variables |
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| Authors: | J. R. Blum M. Brennan |
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| Affiliation: | (1) Division of Statistics, University of California, 95616 Davis, CA, USA;(2) Department of Mathematics, University of Southern California, 90007 Los Angeles, CA, USA |
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| Abstract: | Let {X n} n =1/∞ be a sequence of random variables with partial sumsS n, and let {ie241-1} be the σ-algebra generated byX 1,…,X n. Letf be a function fromR toR and suppose {ie241-2}. Under conditions off and moment conditions on theX' ns, we show thatS n/n converges a.e. (almost everywhere). We give several applications of this result. Research supported by N.S.F. Grant MCS 77-26809 |
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