  Let $X$ be a continuous-time strongly mixing or weakly dependent process and
$T$ a renewal process independent of $X$ with inter-arrival times $\tau$. We
show general conditions under which the sampled process
$(X_{T_i},T_i-T_{i-1})^{\top}$ is strongly mixing or weakly dependent.
Moreover, we explicitly compute the strong mixing or weak dependence
coefficients of the renewal sampled process and show that exponential or power
decay of the coefficients of $X$ is preserved (at least asymptotically). Our
results imply that essentially all central limit theorems available in the
literature for strongly mixing or weakly dependent processes can be applied
when renewal sampled observations of the process $X$ are at disposal.
