Speed of convergence to an extreme value distribution for non-uniformly hyperbolic dynamical systems
Speed of convergence to an extreme value distribution for non-uniformly hyperbolic dynamical systems
复制标题
非均匀双曲动力系统收敛到极值分布的速度
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
M. Nicol
中科院分区：
文献类型：
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作者：
M. Holland;M. Nicol
设(f，？，ν)是一个动力系统，ϕ：？→ℝ是在？中的(一般)点具有唯一极大值的观测。我们考虑连续极大值的时间序列：=max{ϕ(X)，…、ϕ◦Fn-1(X)}。最近的工作集中于这种极大值(在适当的正规化下)到极值分布的分布收敛。对于某些动力系统，我们建立了极限分布的收敛速度。与I.I.D.的情况形成对比。对于随机变量，收敛速度取决于混合速度和重复时间统计量。对于一系列的应用，包括一致扩展映射、二次映射和间歇映射，我们建立了相应的收敛速度。我们还建立了某些双曲型系统，如Anosov系统的收敛速度，并讨论了非一致双曲型系统，如Henon映射的收敛速度。
Suppose (f, ?, ν) is a dynamical system and ϕ : ? → ℝ is an observation with a unique maximum at a (generic) point in ?. We consider the time series of successive maxima Mn(x) := max{ϕ(x),…,ϕ ◦ fn-1(x)}. Recent works have focused on the distributional convergence of such maxima (under suitable normalization) to an extreme value distribution. In this paper, for certain dynamical systems, we establish convergence rates to the limiting distribution. In contrast to the case of i.i.d. random variables, the convergence rates depend on the rate of mixing and the recurrence time statistics. For a range of applications, including uniformly expanding maps, quadratic maps, and intermittent maps, we establish corresponding convergence rates. We also establish convergence rates for certain hyperbolic systems such as Anosov systems, and discuss convergence rates for non-uniformly hyperbolic systems, such as Henon maps.
影响因子：
4
作者：
Holland, Mark P.;Vitolo, Renato;Broer, Henk W.
通讯作者：
Broer, Henk W.