Timeline for Wiener process related counterexample
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
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| Sep 25, 2010 at 19:36 | comment | added | Reda | Indeed... In Byron's construction, every path is being broken at a random point T. However, if i choose in advance $t_0, t_1, \dots, t_n$ and look at the joint law of $(W_{t_0}, \dots, W_{t_n})$, there is no chance $T$ is one of $t_0, t_1, \dots, t_n$, so the law is the same. I can take n arbitrarily big also (if T has density, i can look at all rational times at the same time...). I just changed $W_T$, which accounts for a set of measure zero. | |
| Sep 25, 2010 at 17:58 | comment | added | Cosmonut | Hello Byron and Reda, thanks for replying. Just one thing which is confusing me a little. Reda says, "Byron exhibited another version by changing the process on a set of measure zero". Intuitively, what I understand of Byron's construction is that every path is being broken "at a different point in time". Thus, all the paths are discontinuous, but the joint distributions of the random variables W(t) remain unchanged. Is that what you mean as well ? | |
| Sep 25, 2010 at 13:43 | comment | added | user6096 | Very nice explanation! | |
| Sep 25, 2010 at 7:46 | history | answered | Reda | CC BY-SA 2.5 |