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Absolute continuity between the Wiener and stationary Gaussian measures

Keich, U. (1999) Absolute continuity between the Wiener and stationary Gaussian measures. Pacific Journal of Mathematics, 188 (1). pp. 95-108. ISSN 0030-8730. http://resolver.caltech.edu/CaltechAUTHORS:KEIpjm99a

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Abstract

It is known that the entropy distance between two Gaussian measures is finite if, and only if, they are absolutely continuous with respect to one another. Shepp (1966) characterized the correlations corresponding to stationary Gaussian measures that are absolutely continuous with respect to the Wiener measure. By analyzing the entropy distance, we show that one of his conditions, involving the spectrum of an associated operator, is essentially extraneous, providing a simple criterion for finite entropy distance in this case.


Item Type:Article
Additional Information:© Copyright 1999 Pacific Journal of Mathematics. Received July 6, 1998.
Record Number:CaltechAUTHORS:KEIpjm99a
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:KEIpjm99a
Alternative URL:http://pjm.math.berkeley.edu/1999/188-1/p05.html
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:712
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:16 Sep 2005
Last Modified:26 Dec 2012 08:41

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