Strong deviation theorems for functionals of the nonnegative continuous random variables

By using the approach of Laplace transform, we establish the strong deviation theorems represented by inequalities and described by asymptotic average log-likelihood ratio for functionals of the nonnegative continuous random variables. As corollaries, we obtain several strong laws of large numbers for the random variable functionals. The results of this paper extend and improve the corresponding results of some current literatures.