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1 LSTA - Laboratoire de Statistique Théorique et Appliquée 2 Département de Mathématiques Evry

Abstract : Let G be a topological compact group acting on some space Y. We study a decomposition of Y-indexed stochastic processes, based on the orthogonality relations between the characters of the irreducible representations of G. In the particular case of a Gaussian process with a G-invariant law, such a decomposition gives a very general explanation of a classic identity in law - between quadratic functionals of a Brownian bridge - due to Watson 1961. Several relations with Karhunen-Loève expansions are discussed, and some applications and extensions are given - in particular related to Gaussian processes indexed by a torus.

Keywords : Stochastic processes Topological compact groups Irreducible representations Quadratic functionals Watson-s duplication identity double Wiener-Itô integrals





Author: Giovanni Peccati - Jean-Renaud Pycke -

Source: https://hal.archives-ouvertes.fr/



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