Hilbert space valued Gaussian processes, their kernels, factorizations, and covariance structure
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909274056163328 |
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| author | Jorgensen, Palle E. T. Tian, James |
| author_facet | Jorgensen, Palle E. T. Tian, James |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_14685 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hilbert space valued Gaussian processes, their kernels, factorizations, and covariance structure Jorgensen, Palle E. T. Tian, James Functional Analysis Primary: 46E22. Secondary: 47A20, 47B32, 60G15 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. |
| title | Hilbert space valued Gaussian processes, their kernels, factorizations, and covariance structure |
| topic | Functional Analysis Primary: 46E22. Secondary: 47A20, 47B32, 60G15 |
| url | https://arxiv.org/abs/2404.14685 |