Strong deviation theorems for delayed sums of the nonnegative continuous random variables

Abstract

In this paper, we extend the strong deviation theorems for functions of the nonnegative continuous random variables to the case of delayed sums of the nonnegative continuous random variables, represented by inequalities and described by asymptotic delayed log-likelihood ratio. As corollaries, we obtain several strong law of large numbers for delayed sums of functions of the nonnegative continuous random variables. The results of this manuscript extend and improve the corresponding results of some current literatures.

Keywords:

• Nonnegative continuous random variables
• delayed sums
• generalized log-likelihood ratio
• generalized strong deviation theorems

CLASSIFICATION (MSC 2000):

• 60C05
• 05C80

Additional information

Funding

Research supported by Natural Science Foundation of Zhejiang Province (Grant No. LY17A010013) National Natural Science Foundation of China (Grant No. 11201344) and Wenzhou Bureau of science and technology (Grant No. R20160005).