New challenges related to random field modelling from chaotic expansions

M. D. RUIZ-MEDINA, J. M. Angulo

Random polynomials have been extensively applied in approximation theory in probability and statistics. One of the most outstanding cases corresponds to the chaotic expansion of
Gaussian and Gamma-correlated subordinated random fields. We refer to the general class of Lancaster--Sarmanov random fields. It is well known that their bivariate probability distributions admit a diagonal series expansion in terms of orthogonal polynomials. In this framework, Pearson functional represents the Hilbert-Schmidt operator norm of a kernel involving the bivariate probability density and the tensor product of the marginals, as a measure of the distance to pairwise independence of the random components of the random field. Our proposal extends this statistical distance to pairwise independence, based on the Pearson functional, to mutual independence involving the n-dimensional distributions of the Gamma-correlated random field family analyzed, for n=2k, (k larger or equal to 2).

Keywords: Pearson functional, Gamma-correlated random field, independence, Lancaster–Sarmanov random fields

Stochastic processes and their applications III
June 12, 2025  11:30 AM
Auditorio 2. Leandre Cristòfol

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