The Nonlinear Gaussian Spectrum of Log-normal Stochastic Processes and Variables

A procedure is presented in this paper for developing a representation of lognormal stochastic processes via the polynomial chaos expansion. These are processes obtained by applying the exponential operator to a gaussian process. The Polynomial Chaos expansion results in a representation of a stochastic process in terms of mul-tidimensional polynomials orthogonal with respect to the Gaussian measure with the dimension deened through a set of independent normalized gaussian random variables. Such a representation is useful in the context of the spectral stochastic nite element method, as well as for the analytical investigation of the mathematical properties of lognormal processes.