论文标题
在更新采样下的强烈混合和弱依赖性的继承
Inheritance of strong mixing and weak dependence under renewal sampling
论文作者
论文摘要
让$ x $成为连续的时间强烈混合或弱依赖的过程，而续约过程$ t $独立于$ x $，而到达额度时间$τ$。我们展示了采样过程$（x_ {t_i}，t_i-t_ {i-1}）^{\ top} $在这些条件下，t_i-t_ {i-1}）$强烈混合或微弱依赖。此外，我们明确计算了续订采样过程的强混合或弱依赖系数，并表明该系数的指数或功率衰减是$ x $的（至少是渐近）。我们的结果表明，本质上，当续订对流程$ x $的续订采样观察值时，文献中可用于强烈混合或弱依赖过程的所有中心限制定理都可以应用。
Let $X$ be a continuous-time strongly mixing or weakly dependent process and $T$ a renewal process independent of $X$ with inter-arrival times $τ$. 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.
