论文标题
在任意维度中，Copula测量和SKLAR定理
Copula Measures and Sklar's Theorem in Arbitrary Dimensions
论文作者
论文摘要
尽管用于各种无限二维对象（例如高斯过程和马尔可夫过程），但使用Copulas并定义了Copulas，但尚无对统一这些概念的Copula的普遍概念。我们提出了一种统一的方法，并将Copulas定义为一般产品空间的概率度量。为此，我们在这种无限维度的环境中证明了Sklar的定理。我们展示了如何将此结果传输到各种函数空间设置，并描述了如何在Copulas领域中这些空间中的这些空间进行建模和近似依赖概率度量。
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.
