Limit behaviors for a heavy-tailed β-mixing random sequence∗.

Let {X,Xn, n ≥ 1} be a stationary sequence of nonnegative β-mixing random variables with heavy-tailed distributions, and let Sn = X1 + X2 + · · · + Xn be the partial sums. In the present paper, we establish the logarithmic asymptotic behavior for the tail probability P(Sn> bn) for some b > 1 and the weak law of large numbers for Sn. [ABSTRACT FROM AUTHOR]