Timeline for Uniqueness of the variance
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 15, 2023 at 17:59 | comment | added | Iosif Pinelis | @MateuszKwaśnicki : I see, thank you. | |
| Aug 15, 2023 at 17:54 | comment | added | Mateusz Kwaśnicki | Something like $(\Gamma(-p))^{-1} \int_0^\infty t^{-1-p} (u(t) - u(0) - u'(0)t - \ldots - u^{(k)}(0)t^k/k!) dt$, with $k = \lfloor p\rfloor$. This should be equivalent to the usual definition by $k$-fold integration by parts. | |
| Aug 15, 2023 at 15:03 | comment | added | Iosif Pinelis | @MateuszKwaśnicki : Can you say what exactly you meant by " the Riemann–Liouville fractional derivative of $\ln|f_X|$ at zero"? | |
| Aug 15, 2023 at 10:34 | comment | added | Mateusz Kwaśnicki | At $t=0$, $|f_X(t)|$ is as smooth as $f_X(t)$, I guess. But I did not take time to work out the details, so I may be missing something. | |
| Aug 14, 2023 at 14:58 | comment | added | Iosif Pinelis | @MateuszKwaśnicki : Here may be a problem, though: Even if $f_X$ is smooth, $|f_X|$ does not have to differentiable even once. | |
| Aug 14, 2023 at 1:23 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
added 2 characters in body
|
| Aug 13, 2023 at 21:56 | comment | added | Iosif Pinelis | @MateuszKwaśnicki : Thank you for your comment. | |
| Aug 13, 2023 at 21:43 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
added 103 characters in body
|
| Aug 13, 2023 at 20:15 | comment | added | Mateusz Kwaśnicki | And the same idea — evaluating the Riemann–Liouville fractional derivative of $\ln|f_X|$ at zero — works for larger values of $p$ as long as $X$ has sufficiently many moments. | |
| Aug 13, 2023 at 19:51 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
added 3 characters in body
|
| Aug 13, 2023 at 19:44 | history | answered | Iosif Pinelis | CC BY-SA 4.0 |