DocumentCode :
914018
Title :
A theorem on conditional expectation
Author :
Mazo, J.E. ; Salz, J.
Volume :
16
Issue :
4
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 
be a stationary random process possessing a mean-square derivative 
. Then the conditional ensemble average 
always vanishes.
be a stationary random process possessing a mean-square derivative . Then the conditional ensemble average 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 :
