A theorem on conditional expectation

Author

Mazo, J.E. ; Salz, J.

Volume

Issue

fYear

1970

fDate

7/1/1970 12:00:00 AM

Firstpage

379

Lastpage

381

Abstract

A statistic often encountered in various estimation problems is the conditional ensemble average of the time derivative of a random signal given the signal. It turns out that for a very large class of random signals this statistic is equal to zero. This is a rather surprising result and as far as can be determined has not been precisely stated and rigorously proven. A precise statement and a rigorous proof of this theorem is the subject of this paper. Our result is the following. Let $y(t)$ be a stationary random process possessing a mean-square derivative $\\dot{y}(t)$ . Then the conditional ensemble average $E {\\dot{y}(t)\\mid y(t) }$ always vanishes.

Keywords

Estimation; Stochastic signals; Classification algorithms; Equations; Filters; Information theory; Pattern classification; Pattern recognition; Random processes; Recursive estimation; Statistics; Stochastic processes;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.1970.1054473

Filename

1054473

Link To Document

https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=914018