Timeline for A note on Doob's theorem
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 28 at 2:19 | vote | accept | Alex | ||
| May 10, 2022 at 19:01 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Jan 10, 2022 at 18:06 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Dec 11, 2021 at 16:13 | answer | added | pietro siorpaes | timeline score: 1 | |
| Nov 11, 2014 at 0:53 | comment | added | Alex | @NateEldredge. $E$ is usual Lebesgue integral. Yes you are right, if the lengths of atoms of partition are same then it can be shown $$\underset{t\in J}{\sup}E(|G_{n}(\cdot, t)-f|^{p})\leq 2\underset{|h|\leq \lambda^{n}}{\sup}E(|f(x+ h)-f(x)|^{p})$$. But in the case of different lengths I have got some problem | |
| Nov 10, 2014 at 15:14 | comment | added | Nate Eldredge | Does $E$ here simply mean integration over $[0,1]$ with Lebesgue measure? Intuitively, it seems to me that using martingale methods here is overkill; this looks like it may just need some clever calculus. For instance, if $f$ is continuous you get uniform convergence of $G_n$ to $f$, and the uniform distance between $G_n$ and $f$ depends only on the mesh size and the modulus of continuity of $f$. I don't see offhand how to do the $L^p$ case, though. | |
| Nov 10, 2014 at 12:42 | history | asked | Alex | CC BY-SA 3.0 |