Time and Space Varying Copulas

用于时变退化过程可靠性分析的非同质从属子与Lévy Copulas

Nonhomogeneous Subordinators and Lévy Copulas for Reliability Analysis of Time-Dependent Degradation Processes

本研究针对传统退化模型局限，引入非同质Lévy从属子并结合Lévy Copulas，扩展了退化模型以分析时变退化过程的可靠性，通过数值实例验证了模型在寿命分析中的适用性。

Copula Measures and Sklar's Theorem in Arbitrary Dimensions

Although copulas are used and defined for various infinite-dimensional objects (e.g. Gaussian processes and Markov processes), there is no prevalent notion of a copula that unifies these concepts. We propose a unified approach and define copulas as probability measures on general product spaces. For this we prove Sklar's Theorem in this infinite-dimensional setting. We show how to transfer this result to various function space settings and describe how to model and approximate dependent probability measures in these spaces in the realm of copulas.

Orthogonal decomposition of multivariate densities in Bayes spaces and its connection with copulas

Bayes spaces were initially designed to provide a geometric framework for the modeling and analysis of distributional data. It has recently come to light that this methodology can be exploited to provide an orthogonal decomposition of bivariate probability distributions into an independent and an interaction part. In this paper, new insights into these results are provided by reformulating them using Hilbert space theory and a multivariate extension is developed using a distributional analog of the Hoeffding-Sobol identity. A connection between the resulting decomposition of a multivariate den…

基于生成对抗网络和空间填充设计的Copula近似随机采样方法

A Generative Approach to Quasi-Random Sampling from Copulas via Space-Filling Designs

本文提出利用生成对抗网络和空间填充设计的Copula近似随机采样方法，提升高维情况下采样精度和计算效率，并在风险管理中验证了方法的有效性。

Geometry of Discrete Copulas

Multivariate distributions are fundamental to modeling. Discrete copulas can be used to construct diverse multivariate joint distributions over random variables from estimated univariate marginals. The space of discrete copulas admits a representation as a convex polytope which can be exploited in entropy-copula methods relevant to hydrology and climatology. To allow for an extensive use of such methods in a wide range of applied fields, it is important to have a geometric representation of discrete copulas with desirable stochastic properties. In this paper, we show that the families of ultra…

Copulas and Preserver Problems

Preserver problems concern the characterization of operators on general spaces that leave invariant some categories of subsets or ratios. The most known in the mathematical literature are those of linear preserver problems (LPP) which date back to the ninth century. Here, we treat the preserver problem in the recent and emerging field of copulas. Precisely, we prove that \emph{copula property} is preserved uniquely under increasing transformations.