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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 Th orique 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
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(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
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| 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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