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A Fourier transform is a unique mapping of probability onto the complex plane.A Copula provides a many to many mapping of n probability distributions via their CDFs. Theoretically, there should be away to describe the multivariate join between Fourier transformed marginal distributions. Has anyone seen any papers about defining something similar to a Copula in Fourier space? What problems can people foresee with this approach?Cheers.

Haven't read it but how about thisComputation of copulas by Fourier methods

I don't have access to this article right now but it may interest youJoint characteristic functions construction via copulas

Thanks both of you. The first paper is what I was thinking of (released a couple of days before I asked the question. Hot off the press) as it can be applied to stochastic processes. The second is interesting if you want to look at dependent insurance event risk, or you want to improve some CDO models.