On the Markov transformation of Gaussian processes

2024/12/13 by Armand Ley, Ley, Armand
Computer Science · Engineering · #Advanced Data Processing Techniques #FOS: Mathematics #Gaussian Processes and Bayesian Inference #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2412.10001

openalex publication_date 2024/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a Gaussian process (X_t)_{t \∈ \ℝ}, we construct a Gaussian\n\Markov process with the same one-dimensional marginals using sequences\nof transformations of (X_t)_{t \∈ \ℝ} "made Markov" at finitely many\ntimes. We prove that there exists at least such a Markov transform of (X_t)_{t\n\∈ \ℝ}. In the case the instantaneous decorrelation rate of (X_t)_{t\n\∈ \ℝ} is continuous, we prove that the Markov transform is uniquely\ndetermined and characterized through the same instantaneous decorrelation rate.\n

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