Joint Measures and Cross-Convariance Operators,
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1971
- Accession Number
- AD0725050
Entities
People
- Charles R. Baker
Organizations
- University of North Carolina at Chapel Hill