Complete convergence and records for dynamically generated stochastic processes
Complete convergence and records for dynamically generated stochastic processes
复制标题
动态生成的随机过程的完全收敛和记录
DOI：
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发表时间：
2017
影响因子：
1.3
通讯作者：
M. Magalhaes
中科院分区：
文献类型：
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作者：
A. C. Freitas;J. Freitas;M. Magalhaes
我们认为经验的多维罕见事件点过程，保持跟踪的时间发生的极值观测和它们的严重性，随机过程所产生的动力系统，通过评估一个给定的潜在沿着其轨道。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中存在聚类时，在垂直方向上点的堆积的一个新公式，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。利用完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。最后给出了一个实例，说明了聚类方法对记录时间点过程收敛的影响。
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.