In this paper we prove a theorem on the convergence rate in the Marcinkiewicz-Zygmund strong law for stationary mixing sequences. Our result gives the $r$-quick strong law and the finiteness of moments of the largest excess of boundary crossings for such sequences.
"Convergence Rates and $r$-Quick Versions of the Strong Law for Stationary Mixing Sequences." Ann. Probab. 5 (5) 693 - 706, October, 1977. https://doi.org/10.1214/aop/1176995713