Timeline for Maximal inequality for the average of i.i.d. random variables
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| Nov 15, 2018 at 2:09 | comment | added | fedja | @Xiao The underlying idea is fairly simple: once you have the first $n$ terms, they have little chance to influence the sum more than the next $An$ terms, so you can sort of forget about them and think that you just start all over if $A$ is large enough. Also, by the CLT, the condition $\sum_{j=1}^k Z_j\le kt$ doesn't hold with probability close to $1$ only if the standard deviation $\sqrt k$ of the LHS is larger than the RHS, so there seems to be no point in looking at longer sums. This gives about $\log\frac 1t$ independent attempts to get large, each succeeding with constant probability. | |
| Nov 15, 2018 at 1:49 | comment | added | Xiao | Thank you very much for the nice solution! Is there a motivation behind your approach? The calculation seems like magic to me :) | |
| Nov 15, 2018 at 1:40 | vote | accept | Xiao | ||
| Nov 14, 2018 at 20:02 | history | answered | fedja | CC BY-SA 4.0 |