Timeline for Brownian level sets and continuous functions
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 9, 2019 at 21:00 | comment | added | Mateusz Kwaśnicki | There was a problem with the third "easy-to-do". I added additional details, but some are still missing. | |
| Nov 9, 2019 at 20:58 | history | edited | Mateusz Kwaśnicki | CC BY-SA 4.0 |
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| Nov 9, 2019 at 18:46 | comment | added | Bjørn Kjos-Hanssen | Great, I feel like this could be a paper | |
| Nov 9, 2019 at 18:27 | vote | accept | Bjørn Kjos-Hanssen | ||
| Nov 9, 2019 at 8:45 | comment | added | Mateusz Kwaśnicki | Have you seen the edit at the bottom (the "Easy-to-see 1")? Essentially: $\phi$ is monotone, because it is continuous; and it is continuous, because $\phi(W_t)$ is continuous, and $W_t$ is sufficiently "generic" with probability one. (In fact it is sufficient to know that $W_t$ takes every real value, but that would take longer to write.) | |
| Nov 8, 2019 at 23:46 | comment | added | Mateusz Kwaśnicki | I have added some details to the first two claims without a rigorous proof. | |
| Nov 8, 2019 at 23:46 | history | edited | Mateusz Kwaśnicki | CC BY-SA 4.0 |
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| Nov 8, 2019 at 22:39 | comment | added | Mateusz Kwaśnicki | I have heavily edited the answer. I did not have time to think carefully about the details, so I will not be surprised if it is still wrong. And in any case it is rather sketchy; sorry for that. | |
| Nov 8, 2019 at 22:36 | history | edited | Mateusz Kwaśnicki | CC BY-SA 4.0 |
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| Nov 8, 2019 at 19:55 | comment | added | Mateusz Kwaśnicki | Ah, of course you're right. I somehow thought that $f$ must map level sets of $W_t$ into the level sets of $V_t$ corresponding to the same value. I will think about the fix. | |
| Nov 8, 2019 at 10:32 | history | answered | Mateusz Kwaśnicki | CC BY-SA 4.0 |