Timeline for A generalized Ballot theorem
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 21, 2015 at 4:16 | comment | added | usul | Seems like Etemadi's inequality is related: en.wikipedia.org/wiki/Etemadi%27s_inequality | |
| Oct 20, 2015 at 22:36 | comment | added | Vladimir | Sure! That would be perfect. | |
| Oct 20, 2015 at 22:36 | comment | added | Serguei Popov | Let us continue this discussion in chat. | |
| Oct 20, 2015 at 22:35 | comment | added | Serguei Popov | I mean $S_k\leq \nu k$ etc. | |
| Oct 20, 2015 at 22:33 | comment | added | Vladimir | You mean k < n? | |
| Oct 20, 2015 at 22:23 | comment | added | Serguei Popov | I'm not sure, though, if what I wrote is formally true; however, if you substitute all $<$'s to $\leq$'s in the statement, then it should hold. | |
| Oct 20, 2015 at 22:17 | comment | added | Vladimir | That would be great. | |
| Oct 20, 2015 at 22:09 | comment | added | Serguei Popov | I think it should be true that $$ \frac{1}{n}P[S_n<\nu n] \leq P[S_k<\nu k \text{ for all }k\leq n] \leq P[S_n<\nu n], $$ which is, probably, what you need. The 2nd inequality is evident; as for the 1st one, note that $S_n<\nu n$ implies that there is a cyclic shift of $X_1,\ldots,X_n$ such that $S'_k<\nu k \text{ for all }k\leq n$ for the ``new'' partial sums (just shift to the point where $S_j - \nu j$ is maximized). | |
| Oct 20, 2015 at 22:06 | history | edited | Vladimir | CC BY-SA 3.0 |
fixed typos (S instead of X)
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| Oct 20, 2015 at 21:33 | history | asked | Vladimir | CC BY-SA 3.0 |