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| Auteur principal: | |
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| Format: | Preprint |
| Publié: |
2024
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2412.10001 |
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| _version_ | 1866910743859822592 |
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| author | Ley, Armand |
| author_facet | Ley, Armand |
| contents | Given a Gaussian process $(X_t)_{t \in \mathbb{R}}$, we construct a Gaussian \emph{Markov} process with the same one-dimensional marginals using sequences of transformations of $(X_t)_{t \in \mathbb{R}}$ "made Markov" at finitely many times. We prove that there exists at least such a Markov transform of $(X_t)_{t \in \mathbb{R}}$. In the case the instantaneous decorrelation rate of $(X_t)_{t \in \mathbb{R}}$ is continuous, we prove that the Markov transform is uniquely determined and characterized through the same instantaneous decorrelation rate. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_10001 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Markov transformation of Gaussian processes Ley, Armand Probability Given a Gaussian process $(X_t)_{t \in \mathbb{R}}$, we construct a Gaussian \emph{Markov} process with the same one-dimensional marginals using sequences of transformations of $(X_t)_{t \in \mathbb{R}}$ "made Markov" at finitely many times. We prove that there exists at least such a Markov transform of $(X_t)_{t \in \mathbb{R}}$. In the case the instantaneous decorrelation rate of $(X_t)_{t \in \mathbb{R}}$ is continuous, we prove that the Markov transform is uniquely determined and characterized through the same instantaneous decorrelation rate. |
| title | On the Markov transformation of Gaussian processes |
| topic | Probability |
| url | https://arxiv.org/abs/2412.10001 |