Estimation for the additive Gaussian channel and Monge-Kantorovitch measure transportation

Ali Süleyman Üstünel

Stochastic Processes and their Applications, 2007, vol. 117, issue 9, 1316-1329

Abstract: Let (W,[mu],H) be an abstract Wiener space and assume that Y is a signal of the form Y=X+w, where X is an H-valued random variable, w is the generic element of W. Under the hypothesis of independence of w and X, we show that the quadratic estimate of X, denoted by , is of the form [backward difference]F(Y), where F is an H-convex function on W. We prove also some relations between the quadratic estimate error and the Wasserstein distance between some natural probabilities induced by the shift IH+[backward difference]F and the conditional law of Y given X.

Keywords: Gaussian; channel; Malliavin; calculus; Monge-Kantorovitch; (Kantorovich); measure; transportation; H-convex; functionals; Wasserstein; distance (search for similar items in EconPapers)
Date: 2007
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