Journal article
Operator-valued Gaussian processes and their covariance kernels
Infinite dimensional analysis, quantum probability, and related topics, Vol.27(02), 2350020
08/30/2023
DOI: 10.1142/S0219025723500200
Abstract
In this paper, we discuss a new framework for operator-valued Gaussian processes and their covariance kernels. Our emphasis is four-fold: (i) starting with a positive operator-valued measure (POVM) [Formula: see text], we present algorithms for constructing an associated centered, operator-valued, Gaussian process [Formula: see text] with [Formula: see text] as its covariance kernel; (ii) we present different classes of POVMs, and we examine the corresponding classes of operator-valued Gaussian processes [Formula: see text]; (iii) for the operator-valued Gaussian processes [Formula: see text] at hand, and the non-commutative framework, we present the corresponding Itô-integrals; and we (iv) outline features of the operator-valued setting which are different from the more familiar case of scalar-valued Gaussian processes.
Details
- Title: Subtitle
- Operator-valued Gaussian processes and their covariance kernels
- Creators
- Palle E. T. Jorgensen - University of IowaJames Tian - Mathematical Reviews, 416 4th Street Ann Arbor, MI 48103-4816, USA
- Resource Type
- Journal article
- Publication Details
- Infinite dimensional analysis, quantum probability, and related topics, Vol.27(02), 2350020
- Publisher
- World Scientific
- DOI
- 10.1142/S0219025723500200
- ISSN
- 0219-0257
- eISSN
- 1793-6306
- Language
- English
- Electronic publication date
- 08/30/2023
- Academic Unit
- Mathematics
- Record Identifier
- 9984465559402771
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