Timeline for Show that $\mbox{Var}(\sum_{k=0}^{\infty} \delta\{L_{t-k} > k\}) \leq \mbox{Var}(L)$
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 24, 2017 at 20:24 | vote | accept | HolyMonk | ||
| Jan 24, 2017 at 19:43 | answer | added | Ori Gurel-Gurevich | timeline score: 3 | |
| Jan 24, 2017 at 16:04 | comment | added | HolyMonk | For every fixed $m$ | |
| Jan 24, 2017 at 16:03 | comment | added | Fedor Petrov | For every $m$? Is not $m$ fixed? | |
| Jan 24, 2017 at 15:06 | comment | added | HolyMonk | The idea is to work with an ergodic process and view this far enough in time that we can assume that convergence to the stationary distribution has already occurred. | |
| Jan 24, 2017 at 15:05 | comment | added | HolyMonk | I don't want to have that $X_{n+m}$ and $X_n$ are independent, but I want to have that for every $m$, the map $n \mapsto \mbox{Corr}(X_{n+m}, X_n)$ is constant | |
| Jan 24, 2017 at 15:03 | history | edited | HolyMonk | CC BY-SA 3.0 |
added 18 characters in body
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| Jan 24, 2017 at 14:41 | comment | added | Fedor Petrov | It still seems to be not enough. Assume That $m=3$, $X,T,Z$ are independent i.i.d and your sequence is $ZTT\,TZX\,ZXT\,TZX\, ZXT\,...$. Then $X_n$ and $X_{n+3}$ are always independent, but $Y_1$ and $Y_3$ may have different distribution. | |
| Jan 24, 2017 at 14:33 | comment | added | HolyMonk | I added a condition on $(X_n)_n$, namely that the correlation between $X_n$ and $X_{n+m}$ doesn't depend on $n$. | |
| Jan 24, 2017 at 14:32 | history | edited | HolyMonk | CC BY-SA 3.0 |
added an assumption on $(X_n)_n$
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| Jan 24, 2017 at 14:30 | comment | added | Fedor Petrov | why are $Y$'s identically distributed? | |
| Jan 24, 2017 at 12:53 | history | asked | HolyMonk | CC BY-SA 3.0 |