Conditional Moment Representations for Dependent Random Variables

Wlodzimierz Bryc (University of Cincinnati)

Abstract


The question considered in this paper is which sequences of $p$-integrable random variables can be represented as conditional expectations of a fixed random variable with respect to a given sequence of sigma-fields. For finite families of sigma-fields, explicit inequality equivalent to solvability is stated; sufficient conditions are given for finite and infinite families of sigma-fields, and explicit expansions are presented.

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Pages: 1-14

Publication Date: April 13, 1996

DOI: 10.1214/EJP.v1-7

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