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Seminar on Probability and Statistics
Seminar information archive ～10/17｜Next seminar｜Future seminars 10/18～
| Organizer(s) | Nakahiro Yoshida, Hiroki Masuda, Teppei Ogihara, Yuta Koike |
|---|
2025/10/03
16:00-17:10 Room #123 (Graduate School of Math. Sci. Bldg.)
Freddy Delbaen (ETH Zurich)
Writing Uncorrelated Random Variables as a sum of Independent Random Variables (English)
https://u-tokyo-ac-jp.zoom.us/meeting/register/-kK0DZB6SbeMyAye6ujPeA
Freddy Delbaen (ETH Zurich)
Writing Uncorrelated Random Variables as a sum of Independent Random Variables (English)
[ Abstract ]
With Majumdar I proved that for a random variable $X$ that is uncorrelated to a sigma algebra, there exists a best approximation by a random variable that is independent of the sigma algebra. Inductively we get a series of random variables whose terms are independent of the sigma algebra. We show that this series converge to $X$ in $L^2$. The proof uses the Knott-Smith theorem from transport theory. In an earlier version we could show that convergence took place in $L^1$.
[ Reference URL ]With Majumdar I proved that for a random variable $X$ that is uncorrelated to a sigma algebra, there exists a best approximation by a random variable that is independent of the sigma algebra. Inductively we get a series of random variables whose terms are independent of the sigma algebra. We show that this series converge to $X$ in $L^2$. The proof uses the Knott-Smith theorem from transport theory. In an earlier version we could show that convergence took place in $L^1$.
https://u-tokyo-ac-jp.zoom.us/meeting/register/-kK0DZB6SbeMyAye6ujPeA
