Timeline for Proving a non-stopping time
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Sep 15, 2012 at 9:54 | comment | added | Stéphane Laurent | You have understood my comment: I meant it is more clear to prove that $W_y$ is not a stopping time for an example (such as your example) instead of proving that $W_y$ is not a stopping time for the "generic case" | |
| Sep 15, 2012 at 7:18 | comment | added | Did | Not sure I understand your comment but if one looks for an example where no W_y is a stopping time, then the simpler the better, hence, you could try (X_n) i.i.d. uniform on a finite set. | |
| Sep 15, 2012 at 5:50 | comment | added | Stéphane Laurent | Thanks @did. That's true, in fact we are looking for a counter-example and we should define a specific Markov chain for which the stopping-time property fails to be true. | |
| Sep 15, 2012 at 4:50 | comment | added | Did | Of course this proof is valid in the generic case. But it may happen that for some $x$, $X_2=y$ never happens, then $[W_y=1]=\varnothing$ hence, with respect to $\Pr_x$, the event $[W_y=1]$ does belong to $\mathcal F_1$. | |
| Sep 10, 2012 at 9:54 | history | edited | Stéphane Laurent | CC BY-SA 3.0 |
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| Sep 9, 2012 at 19:45 | comment | added | Moderat | This is rather more advanced than my class, but after looking up some terms, you have taught me quite a lot. +1 | |
| Sep 9, 2012 at 19:44 | vote | accept | Moderat | ||
| Sep 9, 2012 at 18:08 | history | answered | Stéphane Laurent | CC BY-SA 3.0 |