On the integral with respect to the tensor product of two random measures

Authors:
Alain Boudou;Yves Romain
Affiliations:
Institut de Mathématiques, Equipe de Statistique et Probabilités, UMR 5219 CNRS, Université Paul Sabatier, 118 Route de Narbonne, 31062 Toulouse cedex, France;Institut de Mathématiques, Equipe de Statistique et Probabilités, UMR 5219 CNRS, Université Paul Sabatier, 118 Route de Narbonne, 31062 Toulouse cedex, France
Venue:
Journal of Multivariate Analysis
Year:
2010

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Abstract

A Fubini-type formula for the integral with respect to the tensor product of two random measures is established in an intrinsic way. This permits one to consider a convolution product. The results are applied to a stationary continuous random function (which may be multiplicatively written with two stationary components) and to principal component analysis in the frequency domain.