Chaos Expansions: A Review

The aim of this paper is t.o describe recent results on the Wiener-ito decomposition. We focus on a survey of new applications of chaos expansions to functionals ofVViener and Gaussiall processes arising from different fields ofprobability and stochastic processes

Semi-parametric multivariate modelling when the marginals are the same

A model is developed for multivariate distributions which have nearly the same marginals, up to shift and scale. This model, based on "interpolation" of characteristic functions, gives a new notion of "correlation". It allows straightforward nonparametric estimation of the common marginal distribution, which avoids the "curse of dimensionality" present when nonparametically estimating the full multivariate distribution. The method is illustrated with environmental monitoring network data, where multivariate modelling with common marginals is often appropriate