Timeline for On the convergence of a martingale
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| Dec 27, 2023 at 21:15 | comment | added | Greyearl | @ChristopheLeuridan Thanks for your comment. It is actually very close and interesting as well! Indeed, it's not necessarily a true martingale. We can open another thread to study the convergence of $\left(W_{\sigma_t}\right)$. | |
| Dec 27, 2023 at 21:07 | comment | added | Christophe Leuridan | This question is surprinzingly close to the conjecture I made in my partial answer at mathoverflow.net/questions/460751/another-curious-martingale/… However, I think that there is a typo here. The martingale that I considered is $(X_{\sigma_t})_{t \ge 0}$, and not $(W_{A_t})$. It do not know whether this last process is a martingale. | |
| Dec 26, 2023 at 6:26 | history | became hot network question | |||
| Dec 25, 2023 at 23:58 | vote | accept | Greyearl | ||
| Dec 25, 2023 at 23:40 | comment | added | Greyearl | That’s true, it might require a localization argument as the intregrand is not bounded, but it can be proven. Thank you ! | |
| Dec 25, 2023 at 23:37 | comment | added | Thomas Kojar | every Itô integral has zero expectation and so the increment disappears. | |
| Dec 25, 2023 at 23:35 | history | edited | Greyearl | CC BY-SA 4.0 |
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| Dec 25, 2023 at 23:34 | comment | added | Greyearl | Yes, you are right, it is actually $M_t:= B_{A_t}$. I have edited the original post. Can we prove that M is a true martingale? | |
| Dec 25, 2023 at 23:29 | comment | added | Thomas Kojar | actually, are you sure this is the right martingale you have in mind? Shouldn't it be $M_{t}=B_{A_{t}}$ equivalently $M_{\sigma_{t}}=B_{t}$? | |
| Dec 25, 2023 at 22:53 | answer | added | Thomas Kojar | timeline score: 5 | |
| Dec 25, 2023 at 22:44 | history | edited | Greyearl | CC BY-SA 4.0 |
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| Dec 25, 2023 at 22:25 | history | asked | Greyearl | CC BY-SA 4.0 |