Geodesic
Linear estimators and radonifying operators
Teoriâ veroâtnostej i ee primeneniâ, Tome 40 (1995) no. 1, pp. 205-213

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We consider the problem of estimating a signal $Y$ with values in a Banach space based on the observation $X$ with values in another Banach space given their joint Gaussian distribution. Linear estimators are denned to be measurable linear transformations. A characterization of measurable linear transformations with respect to a Gaussian measure by radonifying operators is established. The Bayes estimator $\mathbf{E}(Y|X)$ is shown to be a measurable linear transformation and the associated radonifying operator is derived.
Keywords: radonifying operator, measurable linear transformation, conditional Gaussian distribution. 
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     author = {H. Luschgy},
     title = {Linear estimators and radonifying operators},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {205--213},
     publisher = {mathdoc},
     volume = {40},
     number = {1},
     year = {1995},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TVP_1995_40_1_a17/}
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H. Luschgy. Linear estimators and radonifying operators. Teoriâ veroâtnostej i ee primeneniâ, Tome 40 (1995) no. 1, pp. 205-213. http://geodesic.mathdoc.fr/item/TVP_1995_40_1_a17/