Timeline for Large deviations type results for sum of i.i.d. random functions
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 11, 2015 at 15:58 | comment | added | Serguei Popov | Seems this question was answered here: mathoverflow.net/questions/171527/… (although I'm not totally sure) | |
| Nov 11, 2015 at 15:55 | comment | added | Serguei Popov | @Michael - but we need that $f_k$'s are i.i.d. That, is, $c_k$ shouldn't depend on $k$ then. | |
| Nov 11, 2015 at 15:50 | comment | added | Michael | I should have said $c_k$ constants, which I would say have sub-exponential tails, regardless of how big they may be. But if you accept that you can't expect $X_n$ to be order of $\sqrt n$. | |
| Nov 11, 2015 at 15:39 | comment | added | Serguei Popov | @Michael - yes, if $c_k$ are i.i.d.r.v. with exponential tails. | |
| Nov 11, 2015 at 15:38 | comment | added | Serguei Popov | @Nate Eldredge - not much. $\sum M_k$ just grows linearly with positive speed, and we need to obtain that $\sum f_k$ somehow resembles a sum of 0-mean r.v.'s | |
| Nov 11, 2015 at 15:37 | history | edited | Serguei Popov | CC BY-SA 3.0 |
added 13 characters in body
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| Nov 11, 2015 at 15:17 | comment | added | Michael | Let $Z_i$ be i.i.d. $\pm 1$ random variables. Do $f_k = c_kZ_k$ satisfy your hypotheses ? | |
| Nov 11, 2015 at 15:08 | comment | added | Nate Eldredge | What do you get from the trivial bound $X_n \le \sum_{k=1}^n M_k$? | |
| Nov 11, 2015 at 14:59 | history | asked | Serguei Popov | CC BY-SA 3.0 |