Article ID Journal Published Year Pages File Type
1157057 Stochastic Processes and their Applications 2007 14 Pages PDF
Abstract

Let (W,μ,H)(W,μ,H) be an abstract Wiener space and assume that YY is a signal of the form Y=X+wY=X+w, where XX is an HH-valued random variable, ww is the generic element of WW. Under the hypothesis of independence of ww and XX, we show that the quadratic estimate of XX, denoted by Xˆ(Y)=E[X|Y], is of the form ∇F(Y)∇F(Y), where FF is an HH-convex function on WW. We prove also some relations between the quadratic estimate error and the Wasserstein distance between some natural probabilities induced by the shift IH+∇FIH+∇F and the conditional law of YY given XX.

Related Topics
Physical Sciences and Engineering Mathematics Mathematics (General)
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