Timeline for Simple random walk return time
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Jul 25, 2022 at 13:00 | vote | accept | Rafaël | ||
| Jul 20, 2022 at 13:41 | comment | added | Rafaël | Oh sorry I didn't know there was a difference between stackexchange avec overflow. I guess overflow is more professional in a way ? Thanks anyway ! | |
| Jul 19, 2022 at 23:40 | answer | added | Iosif Pinelis | timeline score: 1 | |
| Jul 19, 2022 at 23:35 | comment | added | James Martin | Probably more suitable at math.stackexchange.com than here, but here are some hints for one approach. The probability that the first return is at time $2n$ is $2^{-2n}$ times the number of Dyck paths of length $2n$. The number of such paths is the $n$th Catalan number $C_n=\frac{1}{n+1}\binom{2n}{n}$, which behaves as $C_n\sim\frac{2^{2n}}{n^{3/2}\sqrt{\pi}}$ as $n\to\infty$. This already gives you $\mathbb{P}(\tau_0^+=2n)\sim Cn^{-3/2}$. For a start on Dyck paths, Catalan numbers, and many related things, you could look at en.wikipedia.org/wiki/Catalan_number . | |
| Jul 19, 2022 at 22:48 | history | edited | Rafaël | CC BY-SA 4.0 |
added 7 characters in body
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| S Jul 19, 2022 at 22:48 | review | First questions | |||
| Jul 19, 2022 at 23:55 | |||||
| S Jul 19, 2022 at 22:48 | history | asked | Rafaël | CC BY-SA 4.0 |