Hilbert space valued Gaussian processes, their kernels, factorizations, and covariance structure

Palle E. T Jorgensen; James Tian

doi:10.48550/arxiv.2404.14685

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Hilbert space valued Gaussian processes, their kernels, factorizations, and covariance structure

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Hilbert space valued Gaussian processes, their kernels, factorizations, and covariance structure

Palle E. T Jorgensen and James Tian

ArXiv.org

Cornell University

04/22/2024

DOI: 10.48550/arxiv.2404.14685

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Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

Abstract

Motivated by applications, we introduce a general and new framework for operator valued positive definite kernels. We further give applications both to operator theory and to stochastic processes. The first one yields several dilation constructions in operator theory, and the second to general classes of stochastic processes. For the latter, we apply our operator valued kernel-results in order to build new Hilbert space-valued Gaussian processes, and to analyze their structures of covariance configurations.

Mathematics - Functional Analysis

Details

Title: Subtitle: Hilbert space valued Gaussian processes, their kernels, factorizations, and covariance structure
Creators: Palle E. T Jorgensen
James Tian
Resource Type: Preprint
Publication Details: ArXiv.org
DOI: 10.48550/arxiv.2404.14685
ISSN: 2331-8422
Publisher: Cornell University; Ithaca, New York
Language: English
Date posted: 04/22/2024
Academic Unit: Mathematics
Record Identifier: 9984618350002771

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