Generation of non-Gaussian tensor-valued random fields using an ISDE-based algorithm

Abstract

This work is concerned with the construction of a random generator for non-Gaussian tensorvalued random fields. Specifically, it focuses on the generation of the class of Prior Algebraic Stochastic Models associated with elliptic operators, for which the family of first-order marginal probability distributions is constructed using the MaxEnt principle. The strategy essentially relies on the definition of a family of diffusion processes, the invariant measures of which coincide with the target system of first-order marginal probability distributions. Those processes are classically defined as the unique stationary solutions of a family of Itô stochastic differential equations, the definition of which involves the construction of a family of normalized Wiener processes. The definition of the later allows spatial dependencies to be generated and the algorithm turns out to be very efficient for high probabilistic dimensions -it does not suffer from the curse of dimensionnality that is inherently exhibited by Gaussian chaos expansions, for instance. The algorithm is finally exemplified through the generation of a matrix-valued non-Gaussian random field.