Timeline for Expectation of first positive value in random walk
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
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| Oct 29, 2010 at 16:45 | history | edited | Did | CC BY-SA 2.5 |
added 252 characters in body; added 74 characters in body
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| Oct 29, 2010 at 16:38 | comment | added | Did | @Louigi, Byron: Argh... You are right, of course; the argument works only if the upward steps are integer valued. Sorry, I shall modify the answer. | |
| Oct 29, 2010 at 15:54 | comment | added | user6096 | @Louigi: You beat me! | |
| Oct 29, 2010 at 15:54 | comment | added | user6096 | @Didier: Why does $S_M=0$ on $X_1>0$? When $p=1/3$, you could jump once to the right, then once left, and find yourself at -1/2. This is the first time that the process is $\leq 0$. However, I'm still hopeful that the Wiener-Hopf approach may lead to a solution! | |
| Oct 29, 2010 at 15:50 | comment | added | Louigi Addario-Berry | This would be right except that it is not necessarily true that $S_M=0$ on the event $X_1 > 0$. If $p=2/3$, for example, then $X$ takes values $-1$ and $1/2$, So $S_M$ can take the value $-1/2$. | |
| Oct 29, 2010 at 15:32 | history | answered | Did | CC BY-SA 2.5 |