Strong Deviation Theorems for the Continuous Random Variables and the Approach of Moment Generating Function

摘要

In virtue of the notion of likelihood ratio, the limit properties of the sequences of continuous random variables are studied ,and a class of strong deviation theorems which represented by inequalities between random variables and their expectation are obtained, hi the proof an approach of applying the tool of moment generation function to the study of strong limit theorem is proposed. As a result, we obtain some deviation theorems for Normal distribution and Gamma distribution.