Variational proof of conditional expectations
Probability
2025-04-01 v1 Optimization and Control
Abstract
In this paper, we show that the conditional expectation of a random variable with finite second moment given a -algebra is the unique critical point of an energy functional in Hilbert space . Then, we extend by density the result to every integrable random variable.
Cite
@article{arxiv.2503.22947,
title = {Variational proof of conditional expectations},
author = {Hugo Guadalupe Reyna Castañeda and María de los Ángeles Sandoval-Romero},
journal= {arXiv preprint arXiv:2503.22947},
year = {2025}
}
Comments
6 pages, 0 figures