Abstract: Let {X_n, n ≥ 1} be a sequence of arbitrary continuous random variables, we introduce the notion of limit asymptotic logarithm likelihood ratio r(ω), as a measure of dissimilarity between probability measure P and reference measure Q. We get some strong deviation theorems for the partial sums of arbitrary continuous random variables under Chung-Teicher’s type conditions [6-7].

Key words: limit asymptotic logarithm likelihood ratio, random sequence, strong deviation
theorem