Convergence rates of tail probabilities for sums under dependence assumptions

Let {X, X 1, X 2, ...} be a zero mean strictly stationary .-mixing sequence. Set S n = . nk=1 X k and f(x p) = . .n=1 n r.2P(|S n | . x p ES2nlogn.........). When . > (2..)1/p, for p > 1/2 and r > 1, the conditions for . . . f(x p dx < . to hold is established, by using coupled methods together with strong approximation, which are different from the traditional symmetrization and Hoffman-Jørgensen inequality.