更新抽样下强混合弱相依的遗传
Inheritance of strong mixing and weak dependence under renewal sampling
摘要：
设$X$是连续时间强混合或弱相依过程，$T$是独立于$X$的更新过程，其到达间隔时间为$τ$ .我们一般的条件下，采样过程$(X_{T_i},T_i-T_{i-1})^{\top}$是强混合或弱依赖。此外，我们明确地计算强混合或弱相关系数的更新采样过程，并表明指数或幂衰减的系数$X$被保存（至少渐近）。我们的研究结果意味着，基本上所有的中心极限定理，在文献中的强混合或弱相关的过程可以应用时，更新采样观察过程$X$是在处置。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
