Geodesic
On a Density of one Gaussian Distribution with Respect to Another
Teoriâ veroâtnostej i ee primeneniâ, Tome 7 (1962) no. 1, pp. 84-89

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In this paper two arbitrary Gaussian measures $P_1(d\omega)$ and $P_2(d\omega)$ of a stochastic process $\{\xi_\alpha(\omega)\}$ with an abstract parameter $\alpha$ are considered. It is proved that they are equivalent if and only if the operator $B$ (in (12)) on the Hilbert space $H$ of random variables (10) has a pure point spectrum, and the eigen-vectors and the eigen-values of $B$ satisy conditions (15) and (16); the density $p(\omega)=P_1(d\omega)/P_2(d\omega)$ satisfies equation (17). 
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     author = {Yu. A. Rozanov},
     title = {On a {Density} of one {Gaussian} {Distribution} with {Respect} to {Another}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {84--89},
     publisher = {mathdoc},
     volume = {7},
     number = {1},
     year = {1962},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1962_7_1_a5/}
}
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Yu. A. Rozanov. On a Density of one Gaussian Distribution with Respect to Another. Teoriâ veroâtnostej i ee primeneniâ, Tome 7 (1962) no. 1, pp. 84-89. http://geodesic.mathdoc.fr/item/TVP_1962_7_1_a5/