Absolute Continuity between the Wienerand Stationary Gaussian
نویسنده
چکیده
It is known that the entropy distance between two Gauss-ian measures is nite 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 nite entropy distance in this case.
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Absolute Continuity between the Wiener and Stationary Gaussian Measures
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 [5] 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 spe...
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