Timeline for Weierstrass' function and Brownian motion
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 22, 2011 at 2:34 | comment | added | john mangual | do random fourier series also converge to brownian motion? | |
| Mar 21, 2011 at 20:29 | comment | added | The Bridge | Hi, I thought Brownian Motion had paths with Hölder exponent strictly inferior to 1/2 almost surely ? | |
| Mar 21, 2011 at 20:09 | comment | added | BSteinhurst | @Pablo - It is worth noting that all those fine path properties that are known for Brownian motion come with the 'almost surely' caveat. So it is not surprising that for a specific path candidate less might be known. | |
| Mar 21, 2011 at 19:21 | answer | added | Shai Covo | timeline score: 3 | |
| Mar 21, 2011 at 19:20 | answer | added | BSteinhurst | timeline score: 3 | |
| Mar 21, 2011 at 19:13 | comment | added | Pablo Shmerkin | I doubt there is a direct connection other than both functions sharing similar properties. There are many functions that have Hölder exponent 1/2 everywhere. I note that it is a well-known open problem to compute the Hausdorff dimension of the graph of the Weierstrass function, while for Brownian images this is well-known to be $3/2$ (this is the conjectured value for the Weierstrass graph when $\alpha=1/2$). This tells us that we don't really understand the shape of the Weierstrass function, while for Brownian motion even very fine geometric information is known. | |
| Mar 21, 2011 at 18:00 | history | asked | Simon Lyons | CC BY-SA 2.5 |