Accession Number : AD0725050

Title :   Joint Measures and Cross-Convariance Operators,

Corporate Author : NORTH CAROLINA UNIV CHAPEL HILL DEPT OF STATISTICS

Personal Author(s) : Baker,Charles R.

Report Date : JAN 1971

Pagination or Media Count : 31

Abstract : Let H1 (resp., H2) be a real and separable Hilbert space with Borel sigma-field Gamma 1 (resp., Gamma 2), and let (H1 x H2, Gamma 1 x Gamma 2) be the product measurable space generated by the measurable rectangles. This paper develops relations between probability measures on (H1 x H2, Gamma 1 x Gamma 2), i.e., joint measures, and the projections of such measures on (H1 x Gamma 1) and (H2 x Gamma 2). In particular, the class of all joint Gaussian measures having two specified Gaussian measures as projections is characterized, and conditions are obtained for two joint Gaussian measures to be mutually absolutely continuous. The cross-covariance operator of a joint measure plays a major role in these results, and these operators are characterized. (Author)

Descriptors :   (*MEASURE THEORY, PROBABILITY), OPERATORS(MATHEMATICS), HILBERT SPACE, INFORMATION THEORY, THEOREMS

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE