Timeline for When do maximum and expectation commute?
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
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| Sep 25, 2012 at 1:41 | vote | accept | martin | ||
| Sep 24, 2012 at 21:15 | answer | added | Dan | timeline score: 14 | |
| Sep 24, 2012 at 9:41 | comment | added | pgassiat | If the supremum on the lhs is attained at $t^*$, then the inequality is strict unless almost surely $G(t^*,X) = \sup_t G(t,X)$. So the obvious condition that the maximum is always attained at the same $t$ is also almost necessary. | |
| Sep 24, 2012 at 2:21 | comment | added | martin | @Yemon Choi: I would like the result to hold for any distribution of $X$, but if you want to impose some conditions on $X$, that's fine. I'm still clueless on how to approach the problem. | |
| Sep 23, 2012 at 18:17 | comment | added | Yemon Choi | Is there anything more you're prepared to specify about $X$? | |
| Sep 23, 2012 at 16:00 | comment | added | martin | Yes, $I$ and $X$ are fixed. I've also added an assumption that $I=[0,1]$. | |
| Sep 23, 2012 at 14:17 | history | edited | martin | CC BY-SA 3.0 |
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| Sep 23, 2012 at 14:11 | history | edited | martin | CC BY-SA 3.0 |
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| Sep 23, 2012 at 14:05 | history | edited | martin | CC BY-SA 3.0 |
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| Sep 23, 2012 at 12:55 | comment | added | Gerald Edgar | I talked with a mathematician once who expressed frustration with some modern theoretical physics writing, exactly because of this point. They would use this without justification, or even without noticing. If the random variable $X$ is constant a.s. it would have been OK (in that setting, at least); and in thermodynamics it often turns out that they are constant; but some physicists would forge ahead, maximizing the r.v. by maximizing instead the expectation. | |
| Sep 23, 2012 at 11:56 | answer | added | Stanislav | timeline score: 3 | |
| Sep 23, 2012 at 9:25 | comment | added | Davide Giraudo | Are $I$ and $X$ fixed? | |
| Sep 23, 2012 at 6:47 | history | asked | martin | CC BY-SA 3.0 |