Year: 2025
Type: preprint
Abstract: In this paper, we show that the conditional expectation of a random variable with finite second moment given a $σ$-algebra is the unique critical point of an energy functional in Hilbert space $L^2$. Then, we extend by density the result to every integrable random variable.
Source: arXiv (Cornell University)
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4416424582
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