Joint work with G. Steinbrecher

This talk will begin by discussing the representation of quantile functions for Monte Carlo simulation as solutions of certain non-linear ordinary and partial differential equations, in particular providing an efficient method for convering Gaussian samples to fat-tailed samples. The PDE representation leads us to a natural generalization to a collection of multivariate distributions in which quite exotic combinations of marginal distributions are coupled together in a natural way. In this way we generate a natural alternative to the copula philosophy, where dependency is generated via suitably coupled stochastic differential equations.

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