Complete convergence for \(\alpha\)-mixing sequence (Q1373814)

The paper deals with the complete convergence of sums \(S_n=X_1+\cdots +X_n\) of stationary \(\alpha\)-mixing random variables \(X_i\). Assuming conditions on the rate of the mixing coefficients and on the finiteness of \(E|X_1|^p\) for some \(p>0\), the author proves the convergence of the infinite series \(\sum_n n^{p\alpha-2} P(|S_n|>\varepsilon n^{\alpha})\) for every \(\varepsilon>0\).