Stochastic processes induced by singular operators

Daniel Alpay, Palle E.T. Jorgensen

Research output: Contribution to journalArticlepeer-review

24 Scopus citations

Abstract

In this article, we study a general family of multivariable Gaussian stochastic processes. Each process is prescribed by a fixed Borel measure on n. The case when is assumed absolutely continuous with respect to Lebesgue measure was studied 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 we consider are typically purely singular. Our proofs rely on the theory of (singular) unbounded operators in Hilbert space, and their spectral theory.

Original languageEnglish
Pages (from-to)708-735
Number of pages28
JournalNumerical Functional Analysis and Optimization
Volume33
Issue number7-9
DOIs
StatePublished - 1 Jan 2012

Keywords

  • Gaussian processes
  • Singular measures
  • Unbounded operators

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