On the Markov transformation of Gaussian processes
Armand Ley · arXiv (Cornell University) · 2024
Given a Gaussian process (X t ) t∈R , we construct a Gaussian Markov process with the same onedimensional marginals using sequences of transformations of (X t ) t∈R "made Markov" at finitely many times. We prove that there exists at least such a Markov transform of (X t ) t∈R . In the case the instantaneous decorrelation rate of (X t ) t∈R is continuous, we prove that the Markov transform is uniquely determined and characterized through the same instantaneous decorrelation rate.