The Arov-Grossman Model and Burg’s Entropy

J.G. Marcano and M.D. Morán
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J.G. Marcano: Universidad de Carabobo, Facultad de Ciencias
M.D. Morán: Universidad Central de Venezuela, Facultad de Ciencias

A chapter in Recent Advances in Applied Probability, 2005, pp 329-349 from Springer

Abstract: Abstract In this paper, we use the connection between the classic trigonometric Caratheodory problem and the maximum entropy Burg problem for a stationary processes to obtain from an Operator Theory point of view: Levinson’s algorithm, Schur’s recursions and the Christoffel-Darboux formula. We deal with a functional model due to Arov and Grossman, which provides a complete description of all minimal unitary extensions of an isometry by the Schur class, in order to describe all the solutions of the Covariance Extension Problem and then we obtain the density that solves the maximum entropy problem of Burg.

Keywords: Apply Probability; Dimensional Hilbert Space; Lebesgue Measure Zero; Isometry Versus; Commutant Lift (search for similar items in EconPapers)
Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-0-387-23394-9_15

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DOI: 10.1007/0-387-23394-6_15

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