Inversion of conditional expectations

James Juei-Chin Yeh

Vol. 52 (1974), No. 2, 631–640

DOI: 10.2140/pjm.1974.52.631

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(e^i(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