Timeline for Are the paths of the Brownian motion contained in a suitable RKHS?
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Jan 5 at 21:46 | answer | added | Kostya_I | timeline score: 1 | |
| Jan 5 at 18:58 | comment | added | Kostya_I | @MarkusLange-Hegermann, unfortunately, it looks like in the BM case, in order to apply their theorem, we would need to find a $\theta$ that satisfies $\theta>\frac12$ and $\theta<\frac12$ simultaneously (unsurprisingly, since their RKHS is just $W^{\theta,2}$ in this case...). | |
| Jan 5 at 18:33 | comment | added | Markus Lange-Hegermann | I think Theorem 4.12 in arxiv.org/abs/1807.02582 does construct such a RKHS that contains paths of the Brownian motion. (I did not check the conditions in detail.) | |
| Jan 5 at 18:06 | comment | added | Kostya_I | Perhaps it is worth mentioning that fractional Sobolev spaces $W^{s,2}$ do not work: $B_t\in W^{s,2}$ almost surely if and only if $s<\frac{1}{2}$, while the point evaluation is continuous if and only if $s>\frac{1}{2}$ | |
| Jan 5 at 16:08 | comment | added | Mueller | Hi, I added some background information. I hope this helps. | |
| Jan 5 at 16:07 | history | edited | Mueller | CC BY-SA 4.0 |
added 1017 characters in body
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| Jan 5 at 13:04 | comment | added | user479223 | What exactly do you mean by RKHS here? Please don't just link the Wiki page... | |
| S Jan 5 at 10:11 | review | First questions | |||
| Jan 5 at 12:06 | |||||
| S Jan 5 at 10:11 | history | asked | Mueller | CC BY-SA 4.0 |