A Max-AR(1) Model with Max-Semistable Marginals

具有类康托尔边缘分布的自动回归过程的极大半稳定极值律

Max-semistable extreme value laws for autoregressive processes with Cantor-like marginals

本文研究边缘分布类似康托尔函数的自动回归过程，证明其边缘分布属于极大半稳定分布的吸引域，并通过引入极值指数得到该过程的极值律，同时揭示其与确定性动力系统极值的联系。

与伯努利卷积相关的AR(1)过程的极大半稳定极端行为

Max-semistable extremal behavior of AR(1)-processes connected with Bernoulli convolutions

本文研究与伯努利卷积相关的AR(1)过程，给出其平稳分布的新结构表示，证明其平稳分布属于极大半稳定律的几何部分吸引域，并得到归一化最大值分布的收敛结果及与动力系统的关联。

具有Fréchet边缘分布的最大稳定随机场的外推

Extrapolation of max-stable random fields with Fréchet marginals

本文提出了一种预测具有α-Fréchet边缘分布H_α的平稳最大稳定随机场的方法，适用于α∈(0,2)的重尾分布，通过水平集外推方法，不依赖矩假设，并建立了 excursion度量与Davis-Resnick距离的联系，证明了预测存在的性，并在多个例子中展示了预报的非唯一性。

Marginal standardization of upper semicontinuous processes. with application to max-stable processes

Extreme-value theory for random vectors and stochastic processes with continuous trajectories is usually formulated for random objects all of whose univariate marginal distributions are identical. In the spirit of Sklar's theorem from copula theory, such marginal standardization is carried out by the pointwise probability integral transform. Certain situations, however, call for stochastic models whose trajectories are not continuous but merely upper semicontinuous (usc). Unfortunately, the pointwise application of the probability integral transform to a usc process does in general not preserv…

Convex geometry of max-stable distributions

It is shown that max-stable random vectors in $[0,\infty)^d$ with unit Fréchet marginals are in one to one correspondence with convex sets $K$ in $[0,\infty)^d$ called max-zonoids. The max-zonoids can be characterised as sets obtained as limits of Minkowski sums of cross-polytopes or, alternatively, as the selection expectation of a random cross-polytope whose distribution is controlled by the spectral measure of the max-stable random vector. Furthermore, the cumulative distribution function $\Prob{ξ\leq x}$ of a max-stable random vector $ξ$ with unit Fréchet marginals is determined by the nor…