3 papers
math.PR2021
A Topological Proof of Sklar's Theorem in Arbitrary Dimensions
Fred Espen Benth, Giulia Di Nunno, Dennis Schroers
We prove Sklar's theorem in infinite dimensions via a topological argument and the notion of inverse systems.
math.PR2020
Copula Measures and Sklar's Theorem in Arbitrary Dimensions
Fred Espen Benth, Giulia Di Nunno, Dennis Schroers
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…
math.PR2020
A weak law of large numbers for realised covariation in a Hilbert space setting
Fred Espen Benth, Dennis Schroers, Almut E. D. Veraart
This article generalises the concept of realised covariation to Hilbert-space-valued stochastic processes. More precisely, based on high-frequency functional data, we construct an…