动态随机过程的全收敛与记录
Complete convergence and records for dynamically generated stochastic processes
摘要：
我们考虑经验多维稀有事件点过程，对于由动力系统产生的随机过程，通过评估沿其轨道的给定势，跟踪极端观测的时间发生及其严重程度。这在不存在和存在聚类的情况下都是如此。本文给出了二维极限点过程在有聚类时垂直方向上点的堆积公式，并推广到高维情形。有限的多维过程计算系统的相关性衰减足够快。利用全收敛结果研究了聚类对极值过程、记录时间和记录值点过程收敛性的影响。给出了聚类阻止记录时间点过程收敛的示例。
英文摘要：
We consider empirical multi-dimensional Rare Events Point Processes that keep track both of the time occurrence of extremal observations and of their severity, for stochastic processes arising from a dynamical system, by evaluating a given potential along its orbits. This is done both in the absence and presence of clustering. A new formula for the piling of points on the vertical direction of bi-dimensional limiting point processes, in the presence of clustering, is given, which is then generalised for higher dimensions. The limiting multi-dimensional processes are computed for systems with sufficiently fast decay of correlations. The complete convergence results are used to study the effect of clustering on the convergence of extremal processes, record time and record values point processes. An example where the clustering prevents the convergence of the record times point process is given.
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