Timeline for Intersection of Brownian motion and finite variation process
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 29, 2023 at 5:32 | comment | added | Nate River | Something is wrong with what I wrote above, but I can’t tell what… | |
| May 29, 2023 at 2:22 | comment | added | Nate River | I have read the linked paper, and have a question about the result for Brownian motion - isn’t it true that Theorem 4.3 implies that the result for Brownian motion may be extended to the critical $\beta = \alpha$ case? Specifically, using the fact that the BM is in $\mathcal A_n (\gamma, 2)$ for all $\gamma < \alpha$ and large enough $n$, and sending $\gamma \to \alpha^-$, we deduce that almost surely there exists no set $A$ on which the BM is $\alpha$ Hölder continuous and $\bar{\text{dim}}_M (A) > 1 - \alpha$. I may be making a mistake though… | |
| Feb 6, 2022 at 19:49 | comment | added | Yuval Peres | No, the set $S$ in the Theorem is allowed to be random (and depend on the BM). | |
| Feb 6, 2022 at 5:11 | comment | added | Nate River | I see! Though there is actually one subtlety - the set on which $B_t = A_t$ is random, while in the theorem $S$ is deterministic. Does this affect anything at all? | |
| Feb 5, 2022 at 16:43 | comment | added | Yuval Peres | This is not discussed in the book- the relevant work was done well after the book was published. | |
| Feb 4, 2022 at 7:17 | comment | added | Nate River | Ah, I wonder if I had missed this in your Brownian motion book… | |
| Feb 4, 2022 at 7:17 | vote | accept | Nate River | ||
| Feb 4, 2022 at 5:36 | history | answered | Yuval Peres | CC BY-SA 4.0 |