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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