Journal article
Stochastic Processes Induced by Singular Operators
Numerical Functional Analysis and Optimization: Operator Algebras and Representation Theory: Frames, Wavelets, and Fractals, Vol.33(7-9), pp.708-735
07/01/2012
DOI: 10.1080/01630563.2012.682132
Abstract
In this article, we study a general family of multivariable Gaussian stochastic processes. Each process is prescribed by a fixed Borel measure σ on ℝ n . The case when σ 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 σ we consider are typically purely singular. Our proofs rely on the theory of (singular) unbounded operators in Hilbert space, and their spectral theory.
Details
- Title: Subtitle
- Stochastic Processes Induced by Singular Operators
- Creators
- Daniel Alpay - Department of Mathematics , Ben Gurion University of the NegevPalle E. T Jorgensen - Department of Mathematics , MLH The University of Iowa
- Resource Type
- Journal article
- Publication Details
- Numerical Functional Analysis and Optimization: Operator Algebras and Representation Theory: Frames, Wavelets, and Fractals, Vol.33(7-9), pp.708-735
- DOI
- 10.1080/01630563.2012.682132
- ISSN
- 0163-0563
- eISSN
- 1532-2467
- Publisher
- Taylor & Francis Group
- Language
- English
- Date published
- 07/01/2012
- Academic Unit
- Mathematics
- Record Identifier
- 9983985937902771
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