{
  "id": "2412.10001",
  "version": "v1",
  "published": "2024-12-13T09:39:50.000Z",
  "updated": "2024-12-13T09:39:50.000Z",
  "title": "On the Markov transformation of Gaussian processes",
  "authors": [
    "Armand Ley"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-12-13T09:39:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "gaussian process",
      "markov transformation",
      "instantaneous decorrelation rate",
      "one-dimensional marginals"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}