A class of strong deviation theorems for continuous random variables sequence

摘要

Purpose - The purpose of this paper is to obtain some strong deviation theorems for arbitrary continuous random variable sequences under suitable restrict Chung-Teicher type conditions. Design/methodology/approach - The crucial part of the proof is to construct a.s. convergence super-martingale by means of the notion of limit logarithmic likelihood ratio of random variable sequences and then applying the martingale convergence theorem. Findings - The upper and lower bounds of the deviations from the sums of arbitrary continuous random sequence to their marginals are obtained. Research limitations/implications - The rigorous bounds are the main limitations which are difficult to obtain. Practical implications - A useful method to study the property of dependent random sequence. Originality/value - The paper presents the new approach of proof strong limit theorems.