Multipoint Schur algorithm, II: generalized moment problems, Gaussian processes and prediction

2010/07/08 by Laurent Baratchart, Baratchart, L., Leonid Golinskiĭ +3
Mathematics · Physics and Astronomy · #30B70 (Secondary) #30E05 (Primary) #60G15 #Cold Atom Physics and Bose-Einstein Condensates #FOS: Mathematics #Probability (math.PR) #Quantum optics and atomic interactions #Random Matrices and Applications #Spectral Theory (math.SP)

paper · pdf · doi:10.48550/arxiv.1007.1363

openalex publication_date 2010/07/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We use nowdays classical theory of generalized moment problems by Krein-Nudelman [1977] to define a special class of stochastic Gaussian processes. The class contains, of course, stationary Gaussian processes. We obtain a spectral representation for the processes from this class and we solve the corresponding prediction problem. The orthogonal rational functions on the unit circle lead to a class of Gaussian processes providing an example for the above construction.

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