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摘要翻译：
我们考虑了由$f_{a}(x)=1-ax^2$给出的具有$x\in[-1,1]$的二次映射族，其中$a$是Benedicks-Carleson参数。对于每一个混沌动力系统，我们研究了由$x_{n}=f_a^n$给出的平稳随机过程$x_0，X_1，...$对于每个整数$n\geq0$的极值分布，其中每个随机变量$x_n$按$f_a$唯一的绝对连续不变概率分布。利用Benedicks和Carleson所发展的技术，我们证明了$m_n=\max\{X_0，...，X_{n-1}}$的极限分布与如果序列$X_0，X_1，...$独立同分布时的极限分布相同。这一结果使我们可以得出$m_n$的渐近分布为III型（Weibull）分布。
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英文标题：
《Extreme values for Benedicks-Carleson quadratic maps》
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作者：
Ana Cristina Moreira Freitas, Jorge Milhazes Freitas
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最新提交年份：
2010
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分类信息：
一级分类：Mathematics 数学
二级分类：Dynamical Systems 动力系统
分类描述：Dynamics of differential equations and flows, mechanics, classical few-body problems, iterations, complex dynamics, delayed differential equations
微分方程和流动的动力学，力学，经典的少体问题，迭代，复杂动力学，延迟微分方程
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一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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一级分类：Mathematics 数学
二级分类：Statistics Theory 统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Statistics 统计学
二级分类：Statistics Theory 统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
We consider the quadratic family of maps given by $f_{a}(x)=1-a x^2$ with $x\in [-1,1]$, where $a$ is a Benedicks-Carleson parameter. For each of these chaotic dynamical systems we study the extreme value distribution of the stationary stochastic processes $X_0,X_1,...$, given by $X_{n}=f_a^n$, for every integer $n\geq0$, where each random variable $X_n$ is distributed according to the unique absolutely continuous, invariant probability of $f_a$. Using techniques developed by Benedicks and Carleson, we show that the limiting distribution of $M_n=\max\{X_0,...,X_{n-1}\}$ is the same as that which would apply if the sequence $X_0,X_1,...$ was independent and identically distributed. This result allows us to conclude that the asymptotic distribution of $M_n$ is of Type III (Weibull).
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PDF链接：
https://arxiv.org/pdf/706.3071
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