On strong deviation theorems concerning array of dependent random sequence

Let xi={xi(ni),1 <= i <= n}(n is an element of N) be an array of random variables on the probability space (Omega,F,P). Let Q be another probability measure on F and, assume that under the law of Q, xi is row-wise independent. Let h(P parallel to Q) be the sample-divergence rate of P with respect to Q related to xi. A kind of strong deviation theorems, represented by h(P parallel to Q), of the arithmetic mean and the geometric mean of xi are obtained. Moreover, no conditions are imposed on the joint distribution of xi.