Timeline for Distributional equation X+Y=2X
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 25, 2016 at 3:31 | history | edited | Gagar | CC BY-SA 3.0 |
edited title
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| May 24, 2016 at 13:04 | vote | accept | Gagar | ||
| May 24, 2016 at 10:07 | answer | added | Victor Kleptsyn | timeline score: 13 | |
| May 24, 2016 at 7:57 | comment | added | Gagar | The fact that the variable is positive should play a crucial role, otherwise one may take a Cauchy random variable (which even does not have an expectation), and there exists solutions which even are not stable random variables (see Feller, An Introduction to Probability Theory and Its Applications Volume 2, chapter XVII.3 (f)) | |
| May 24, 2016 at 7:48 | comment | added | Brendan McKay | I don't see how to prove the variance is finite. The issue is whether functions of the form $e^{ict}$ are the only characteristic functions satisfying $\phi(t)^2=\phi(2t)$ for all $t$. It seems likely. | |
| May 24, 2016 at 7:36 | comment | added | Gagar | And what if there is no variance ;-)? | |
| May 24, 2016 at 7:23 | comment | added | user35593 | From this equation you can conclude that the variance is zero and hence that $X$ is (almost surely) constant. | |
| May 24, 2016 at 6:03 | history | asked | Gagar | CC BY-SA 3.0 |