  Let $\{B(\xi_n,r_n)\}_{n\ge1}$ be a sequence of random balls whose centers
$\{\xi_n\}_{n\ge1}$ is a stationary process, and $\{r_n\}_{n\ge1}$ is a
sequence of positive numbers decreasing to 0. Our object is the random covering
set $E=\limsup\limits_{n\to\infty}B(\xi_n,r_n)$, that is, the points covered by
$B(\xi_n,r_n)$ infinitely often. The sizes of $E$ are investigated from the
viewpoint of measure, dimension and topology.
