Joint Measures and Cross-covariance Operators Jon·it I"leasures and Cross-covariance Operators Joint L"leasljres and Cross-covariance Operators*
نویسنده
چکیده
Let HI (resp., HZ) be a real and separable Hilbert space with Borel a-field f 1 (resp., f 2), and let (HIXH Z ' f 1 x f 2) be the product measurable space generated by the measurable rectangles. This paper develops relations between probability measures on (HIXH Z ' f 1 x f 2), i.e., joint measures, and the projections of such measures on (HI' f 1) and (HZ' f 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.
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تاریخ انتشار 1971