On the equivalence of the measures induced by banach valued gaussian autoregressive processes

Authors: Denis Bosq ^a; Tahar Mourid ^b

Affiliations:	^a Laboratoire de Statistique Thorique et Appliquee, Universit Pierre et Marie Curie, Paris, cedex 05, France
	^b Dpartement de Mathmatiques, Institut des Sciences Exactes, Universit de Tlemcen, Algeria

DOI: 10.1080/07362999908809594

Publication Frequency: 6 issues per year

Published in: journal

Stochastic Analysis and Applications, Volume 17, Issue 2 1999 , pages 137 - 144

Subjects: Statistics & Probability; Stochastic Models & Processes;

Formats available: PDF (English)

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Abstract

We provide a necessary and sufficient condition for the equivalence of the measures generated by Banach valued Gaussian autoregressive processes. This condition requires an Hilbert-Schmidt condition upon autoregressive operators which is automatically satisfied in finite dimension. We derive formulas for the Radon-Nikodym derivative useful in maximum likelihood estimation

Keywords: Probability On Banach Spaces; Banach-Valued Autoregressive Processes; Spectrum; Covariance Operator; Cross Variance Operator; Bounded Operators; Hilbert-Schmidt Condition; Yule-Walker Equations

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On the equivalence of the measures induced by banach valued gaussian autoregressive processes

Abstract