Timeline for The conditions in the definition of Brownian motion
Current License: CC BY-SA 2.5
17 events
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| Sep 16, 2021 at 17:27 | history | wiki removed | Stefan Kohl♦ | ||
| Oct 22, 2010 at 10:50 | vote | accept | Shai Covo | ||
| Oct 22, 2010 at 0:26 | answer | added | George Lowther | timeline score: 11 | |
| Oct 21, 2010 at 19:49 | comment | added | Nate Eldredge | @George Lowther: Great, I will be interested to see it. If one can answer my question more generally with $n$ random variables, then one could probably plug the resulting joint distributions into Kolmogorov's extension theorem and produce a counterexample to the original question. | |
| Oct 21, 2010 at 18:03 | comment | added | George Lowther | Nate - The answer to that is no. The answer to the original question is no, W need not be a BM. I have a (slightly messy) construction of a counterexample in mind, which I'll post when I have a few moments free. | |
| Oct 21, 2010 at 15:15 | comment | added | Nate Eldredge | A special case that might be useful to consider first: if $X$ and $Y$ are separately normally distributed and uncorrelated, and $X+Y$ is also normally distributed, must $(X,Y)$ be jointly normally distributed? | |
| Oct 21, 2010 at 13:29 | history | edited | Shai Covo | CC BY-SA 2.5 |
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| Oct 21, 2010 at 7:56 | history | edited | Bjørn Kjos-Hanssen |
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| Oct 21, 2010 at 7:32 | answer | added | The Bridge | timeline score: 0 | |
| Oct 21, 2010 at 7:08 | history | edited | Shai Covo | CC BY-SA 2.5 |
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| Oct 21, 2010 at 6:13 | history | edited | Shai Covo | CC BY-SA 2.5 |
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| Oct 21, 2010 at 6:00 | history | asked | Shai Covo | CC BY-SA 2.5 |