On the Markov transformation of Gaussian processes
Abstract
Given a Gaussian process (Xt)t ∈ R, we construct a Gaussian Markov process with the same one-dimensional marginals using sequences of transformations of (Xt)t ∈ R "made Markov" at finitely many times. We prove that there exists at least such a Markov transform of (Xt)t ∈ R. In the case the instantaneous decorrelation rate of (Xt)t ∈ R is continuous, we prove that the Markov transform is uniquely determined and characterized through the same instantaneous decorrelation rate.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.