Vol. 52, No. 2, 1974

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Inversion of conditional expectations

James Juei-Chin Yeh

Vol. 52 (1974), No. 2, 631–640
Abstract

By its definition a conditional expectation is the RadonNikodym derivative of a finite signed measure. In this paper an inversion formula is given for recapturing E(Y |X) as an inverse Fourier transform of the function E(ei(u,X)Y ),u Rn, where X is an random vector and Y is a random variable satisfying some regularity conditions.

Mathematical Subject Classification 2000
Primary: 60A10
Secondary: 60E05
Milestones
Received: 13 August 1973
Published: 1 June 1974
Authors
James Juei-Chin Yeh