Absolute continuity between the Wiener and stationary Gaussian measures

U. Keich

Vol. 188 (1999), No. 1, 95–108

DOI: 10.2140/pjm.1999.188.95

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.

Milestones

Received: 6 July 1998

Published: 1 March 1999