Timeline for Convergence of a sequence of dependent binomial trials
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 28, 2014 at 4:10 | answer | added | Douglas Zare | timeline score: 1 | |
| Mar 28, 2014 at 2:35 | comment | added | Douglas Zare | I'd expect that the probability will go to $1$ as long as $t$ goes to infinity with $n$. | |
| Mar 28, 2014 at 2:34 | comment | added | Douglas Zare | This appears to model neutral genetic drift. I looked that up and found that for $n$ even, this is called the Wright-Fisher model, and found this question: math.stackexchange.com/questions/585578/… | |
| Mar 28, 2014 at 0:55 | history | edited | JoelO | CC BY-SA 3.0 |
added 55 characters in body
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| Mar 27, 2014 at 23:54 | comment | added | JoelO | Right. $o(1)$ was supposed to be $o_n(1)$; i.e., it approaches $1$ as $n$ grows. For starters, I want to know how fast it converges to $1-1/n$. In particular, what is the probability of stopping with $b_t=0$ for $t =O(\log n)$? | |
| Mar 27, 2014 at 23:26 | comment | added | Douglas Zare | It's a martingale starting at $1$ and ending at $0$ or $n$, so as $t\to \infty$ it ends at $0$ with probability $(n-1)/n$, never $1-o(1)$. Did you mean to ask something else? | |
| Mar 27, 2014 at 23:17 | history | asked | JoelO | CC BY-SA 3.0 |