Copula measures and Sklar's theorem in arbitrary dimensions

Abstract

AbstractAlthough 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 functional analytic framework, show how Sklar's theorem can be applied in certain examples of Banach spaces and provide a semiparametric estimation procedure for second‐order stochastic processes with underlying Gaussian copula.