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引用次数: 0
摘要
为了获得由动力系统产生的重尾静止过程的函数极限定理,我们需要了解过程尾部观测值的聚类模式。最近在动力学系统中引入的一种名为 "pilling process "的结构可以很好地描述这些模式。迄今为止,我们只计算了在单个排斥固定点上最大化的可观测函数的聚类过程。在这里,我们通过考虑相关最大集(即在属于同一轨道的多个点上观测值最大化)来研究更丰富的聚类行为,并在动力学为片断线性和扩展(1 维和 2 维)时计算出了起球过程的明确表达式。
Functional Limit Theorems for Dynamical Systems with Correlated Maximal Sets
In order to obtain functional limit theorems for heavy-tailed stationary processes arising from dynamical systems, one needs to understand the clustering patterns of the tail observations of the process. These patterns are well described by means of a structure called the pilling process introduced recently in the context of dynamical systems. So far, the pilling process has been computed only for observable functions maximised at a single repelling fixed point. Here, we study richer clustering behaviours by considering correlated maximal sets, in the sense that the observable is maximised in multiple points belonging to the same orbit, and we work out explicit expressions for the pilling process when the dynamics is piecewise linear and expanding (1-dimensional and 2-dimensional).
期刊介绍:
The Journal of Statistical Physics publishes original and invited review papers in all areas of statistical physics as well as in related fields concerned with collective phenomena in physical systems.