Convergence Results for Approximation with independent Variables

2024/05/30 by Freddy Delbaen, Delbaen, Freddy, Chitro Majumdar +1 · 1 citation
Mathematics · Computer Science · #Approximation Theory and Sequence Spaces #Matrix Theory and Algorithms #Iterative Methods for Nonlinear Equations

paper · pdf · doi:10.48550/arxiv.2405.19780

Abstract

For a square integrable m-dimensional random variable X on a probability space (Ω,\Fc,Pr) and a sub sigma algebra \Ac, we show that there is a constructive way to represent X-\Er[X|\Ac] as the sum of a series of variables that are independent of \Ac.

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