Copula measures and Sklar's theorem in arbitrary dimensions

Abstract

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 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.