An operator theory approach to the evanescent part of a two-parametric weak-stationary stochastic process
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913445336580096 |
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| author | Burdak, Zbigniew Kosiek, Marek Pagacz, Patryk Słociński, Marek |
| author_facet | Burdak, Zbigniew Kosiek, Marek Pagacz, Patryk Słociński, Marek |
| contents | A new approach to the evanescent part of a two-dimensional weak-stationary stochastic process with the past given by a half-plane is proceed. The classical result due to Helson and Lowdenslager divides a two-parametric weak-stationary stochastic process into three parts. In this paper we describe the most untouchable one - the evanescent part. Moreover, we point out how this part depends on the shape of the past. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_17970 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An operator theory approach to the evanescent part of a two-parametric weak-stationary stochastic process Burdak, Zbigniew Kosiek, Marek Pagacz, Patryk Słociński, Marek Probability Functional Analysis 47B20, 47A13, 60G10, 60G25 A new approach to the evanescent part of a two-dimensional weak-stationary stochastic process with the past given by a half-plane is proceed. The classical result due to Helson and Lowdenslager divides a two-parametric weak-stationary stochastic process into three parts. In this paper we describe the most untouchable one - the evanescent part. Moreover, we point out how this part depends on the shape of the past. |
| title | An operator theory approach to the evanescent part of a two-parametric weak-stationary stochastic process |
| topic | Probability Functional Analysis 47B20, 47A13, 60G10, 60G25 |
| url | https://arxiv.org/abs/2407.17970 |