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 $(X_{T_i},\tau_i)^{\top}$ 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.

翻译：让X美元是一个连续时间强力混合或弱力依赖的过程,让T美元是一个独立于X美元和抵达期间美元=tau美元的一个更新过程。我们展示了抽样过程$(X ⁇ T_i},\tau_i){top}美元高度混合或依赖性强的一般条件。此外,我们明确计算了重新采样过程强大的混合或弱依赖性系数,并表明X美元系数的指数或功率衰减得到了保存(至少是暂时保存 ) 。 我们的结果表明,文献中可用于强烈混合或依赖性弱的进程的所有中心参数基本上都可以在更新对过程的抽样观察时应用 $X美元 。