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In this paper we study a general family of multivariable Gaussian stochastic processes. Each process is prescribed by a fixed Borel measure σ on Rn. The case when σ is assumed absolutely continuous with respect to Lebesgue measure was stud- ied earlier in the literature, when n = 1. Our focus here is on showing how different equivalence classes (defined from relative absolute continuity for pairs of measures) translate into concrete spectral decompositions of the corresponding stochastic processes under study. The measures σ we consider are typically purely singular. Our proofs rely on the theory of (singular) unbounded operators in Hilbert space, and their spectral theory.


This is an Accepted Manuscript of an article published in Numerical Functional Analysis and Optimization, volume 33, issues 7-9, in 2012, available online: DOI: 10.1080/01630563.2012.682132. It may differ slightly from the final version of record.

Peer Reviewed



Taylor & Francis



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