A class of strong deviation theorems for continuous random variables sequence

Abstract

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.

Citation

Chen, W. (2008), "A class of strong deviation theorems for continuous random variables sequence", Kybernetes, Vol. 37 No. 9/10, pp. 1257-1263. https://doi.org/10.1108/03684920810907535