The Wigner distribution of Gaussian tempered generalized stochastic processes
Fuente:
arXiv
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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916909641891840 |
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| author | Wahlberg, Patrik |
| author_facet | Wahlberg, Patrik |
| contents | We define the Wigner distribution of a tempered generalized stochastic process that is complex-valued symmetric Gaussian. This gives a time-frequency generalized stochastic process defined on the phase space. We study its covariance and our main result is a formula for the Weyl symbol of the covariance operator, expressed in terms of the Weyl symbol of the covariance operator of the original generalized stochastic process. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_03493 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Wigner distribution of Gaussian tempered generalized stochastic processes Wahlberg, Patrik Probability Functional Analysis We define the Wigner distribution of a tempered generalized stochastic process that is complex-valued symmetric Gaussian. This gives a time-frequency generalized stochastic process defined on the phase space. We study its covariance and our main result is a formula for the Weyl symbol of the covariance operator, expressed in terms of the Weyl symbol of the covariance operator of the original generalized stochastic process. |
| title | The Wigner distribution of Gaussian tempered generalized stochastic processes |
| topic | Probability Functional Analysis |
| url | https://arxiv.org/abs/2504.03493 |