Strong deviation theorems for the arbitrary stochastic sequence of on Poisson distribution in the generalized gambling system
In this paper, the notion of the limit logarithm likelihood ratio, as a measure of deviation between a sequence of the integer-valued random variables and a sequence of independent random variables with the Pois-son distribution , is introduced. A subset of the sample space is given by restricting the likelihood ratio, and on this subset a class of strong limit theorems for the sequence of arbitrary integer-valued random variables on the generalized gambling system are obtained. As corollaries, a class of the strong laws for sequences of independent random variables with Poisson distributions are obtained.
generalized gambling systemPoisson distributionlikelihood ratio
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万方数据
维普
