Timeline for Lower bound for the $p$-th absolute moment of a sum of random variables
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Feb 20, 2015 at 12:40 | vote | accept | Cm7F7Bb | ||
| Feb 4, 2015 at 14:45 | comment | added | Goulifet | @Omer If the $X_i$ are i.i.d with finite variance (let say $1$), the answer is yes. Indeed, $S_n / \sqrt{n} \rightarrow \mathcal{N}(0,1)$ with the central limit theorem. Hence we have $\mathbb{E} [\lvert S_n/\sqrt{n} \rvert^p] \rightarrow \mathbb{E}[\lvert \mathcal{N}(0,1) \rvert^p]$ and from that $$\mathbb{E}[|S_n|^p] \sim Cn^{p/2}.$$ | |
| Feb 4, 2015 at 13:59 | comment | added | Omer | Is it true that $\mathbb{E} |S_n|^p \geq c n^{p/2-1} \sum \mathbb{E} |X_i|^p$? | |
| Feb 4, 2015 at 10:56 | history | answered | Goulifet | CC BY-SA 3.0 |