The Erdos-Renyi Laws of Large Numbers for Non-Identically DistributedRandom Variables
Citation：
Lin Zhengyan.The Erdos-Renyi Laws of Large Numbers for Non-Identically DistributedRandom Variables[J].Chinese Annals of Mathematics B,1990,11(3):376~383
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Authors：
Lin Zhengyan;
Abstract：
The Erdos-Renyi law of large numbers (1970) is the first important result for asymptotic behaviours of increments of partial sums of a sequence of random variables with span[ClogN]. Some generalizations have been done since then, such as convergence rate of the limit, some results when order of span being either higher or lower than logN. But all these results are only obtained in the case of i. i. d. random variables. This paper aims at the generalization of these results to the case when random variables are independent, but not necessarily identically distributed. To this end Chernoff Theorem is generalized to the corresponding case at first.
