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

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  • Üstünel, Ali Süleyman

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.

Suggested Citation

  • Üstünel, Ali Süleyman, 2007. "Estimation for the additive Gaussian channel and Monge-Kantorovitch measure transportation," Stochastic Processes and their Applications, Elsevier, vol. 117(9), pages 1316-1329, September.
    • Handle: RePEc:eee:spapps:v:117:y:2007:i:9:p:1316-1329
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