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Vietnam
Journal of Mathematics 39:4 (2011) 405423

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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