摘要
The Erdos-Renyi law of large numbers (1970) is the first important result forasymptotic behaviours of increments of partial sams of a sequence of random variableswith apan [ClogN]. Some generalizations have been done sinoe then, such as conver-gence rate of the limit, some results when order of span being either higher or lowerthan log N. 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 ease when random variablesare independent, but not necessarily identically distributed. To this end Chernoff Theoremis generalized to the corlesponding case at first.
The Erdos-Renyi law of large numbers (1970) is the first important result for asymptotic behaviours of increments of partial sams of a sequence of random variables with apan [ClogN]. Some generalizations have been done sinoe then, such as conver- gence rate of the limit, some results when order of span being either higher or lower than log N. 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 ease when random variables are independent, but not necessarily identically distributed. To this end Chernoff Theorem is generalized to the corlesponding case at first.
基金
Supported by the National Science Fondation.
