Stochastic processes induced by singular operators

Daniel Alpay, Palle E.T. Jorgensen

Research output: Contribution to journalArticlepeer-review

33 Scopus citations


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
Issue number7-9
StatePublished - 1 Jan 2012


  • Gaussian processes
  • Singular measures
  • Unbounded operators

ASJC Scopus subject areas

  • Analysis
  • Signal Processing
  • Computer Science Applications
  • Control and Optimization


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