Timeline for Connections between martingales and Fourier analysis
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 27, 2018 at 20:25 | comment | added | Iosif Pinelis | @MarkMeckes : Thank you for your comment. Of course, if arbitrary functions of the r.v.'s are allowed, then one can express the independence of r.v.'s $X$ and $Y$ as the orthogonality of the centered r.v.'s $f(X)$ and $g(Y)$ for all Borel-measurable $f$ and $g$ such that $f(X)$ and $g(Y)$ are in $L^2$. In fact, it is enough here to take $f$ and $g$ to be the Borel-measurable indicators. However, I don't think Fourier analysis extends even to such indicators of the functions $e^{ik\cdot}$. | |
| Sep 27, 2018 at 16:12 | comment | added | Mark Meckes | There is no way to translate mere orthogonality into independence or even into a martingale condition. True, but on the other hand, there is a connection worth knowing: mathoverflow.net/a/16517/1044 | |
| Sep 24, 2018 at 23:53 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
added 661 characters in body
|
| Sep 20, 2018 at 17:37 | history | answered | Iosif Pinelis | CC BY-SA 4.0 |