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Vietnam Journal of Mathematics 39:4 (2011) 405-423

 

A kind of Random Deviation Theorems for Stochastic Sequence

on Random Selection Systems and Laplace Transforms

Kangkang Wang

School of Mathematics and Physics, Jiangsu

University of Science and Technology, Zhenjiang 212003, China

 

Abstract. In this paper, the notion of asymptotic logarithmic likelihood ratio, as a measure of dissimilarity between the joint distribution density function and the marginal product density function, is introduced. A kind of strong limit theorems represented by inequalities for the dependent nonnegative stochastic sequence on the random selection system are obtained by using the tools of Laplace transform and the differentiation on a net. The bounds given by the theorems depend on sample points. Some results obtained are generalized.

2000 Mathematics Subject Classification: 60F15.

Keywords: Stochastic sequence, asymptotic logarithmic likelihood ratio, random deviation theorem, the differentiation on a net, Laplace transform.

 

 

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