On the Markov transformation of Gaussian processes

Armand Ley

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arXiv · 2412.10001

On the Markov transformation of Gaussian processes

Armand Ley

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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.

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BibTeX RIS

Armand Ley. 2024-12-13. On the Markov transformation of Gaussian processes. https://arxiv.org/abs/2412.10001

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