Conditional moment representations for dependent random variables

  title={Conditional moment representations for dependent random variables},
  author={Wlodzimierz Bryc},
Abstact: 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 σ-fields. For finite families of σ-fields, explicit inequality equivalent to solvability is stated; sufficient conditions are given for finite and infinite families of σ-fields, and explicit expansions are presented. 

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