Timeline for Can an a.s. non constant continuous martingale be differentiable with nonzero probability?
Current License: CC BY-SA 4.0
16 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 21, 2022 at 17:07 | vote | accept | Nate River | ||
| Nov 21, 2022 at 17:07 | vote | accept | Nate River | ||
| Nov 21, 2022 at 17:07 | |||||
| S Nov 21, 2022 at 16:28 | history | bounty ended | Nate River | ||
| S Nov 21, 2022 at 16:28 | history | notice removed | Nate River | ||
| Nov 20, 2022 at 17:41 | answer | added | Christophe Leuridan | timeline score: 1 | |
| S Nov 19, 2022 at 14:19 | history | bounty started | Nate River | ||
| S Nov 19, 2022 at 14:19 | history | notice added | Nate River | Draw attention | |
| S Jan 25, 2022 at 10:00 | history | bounty ended | CommunityBot | ||
| S Jan 25, 2022 at 10:00 | history | notice removed | CommunityBot | ||
| Jan 23, 2022 at 15:16 | comment | added | Tobsn | Intuitively I would expect that by Martingale representation theorem all such processes can be realised as Ito integrals and are therefore indeed not differentiable a.s. | |
| S Jan 17, 2022 at 8:23 | history | bounty started | Nate River | ||
| S Jan 17, 2022 at 8:23 | history | notice added | Nate River | Draw attention | |
| Jan 4, 2022 at 22:29 | comment | added | jlewk | I stand corrected @StephanSturm. The question should link to mathoverflow.net/questions/397639/… | |
| Jan 4, 2022 at 14:37 | comment | added | Stephan Sturm | @jlewk: While the argument is formally correct, I do not think it is useful here. A Lipschitz martingale is of bounded total variation, hence of zero quadratic variation. So the only martingales satisfying this conditions are constants anyway. | |
| Jan 4, 2022 at 3:43 | comment | added | jlewk | $E[M_{t+h}-M_t|F_t] =0$ by the martingale property, but on the other hand, $E[h^{-1}(M_{t+h}-M_t)|F_t]\to^{h\to 0} M_t'$ by dominated convergence if you additionally assume that $M_t$ is $C$-Lipschitz almost surely. So $M_t'=0$ necessarily in this case. | |
| Jan 3, 2022 at 23:52 | history | asked | Nate River | CC BY-SA 4.0 |