Timeline for Continuity of a Functional
Current License: CC BY-SA 3.0
16 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 26, 2014 at 18:22 | vote | accept | Dinesh | ||
| Nov 26, 2014 at 18:22 | vote | accept | Dinesh | ||
| Nov 26, 2014 at 18:22 | |||||
| Nov 26, 2014 at 17:57 | answer | added | Martin Hairer | timeline score: 1 | |
| Nov 26, 2014 at 11:33 | comment | added | Dinesh | So, basically, $M$ can be considered as having support $[\alpha,1-\alpha],\alpha>0$ | |
| Nov 26, 2014 at 11:32 | history | edited | Dinesh | CC BY-SA 3.0 |
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| Nov 26, 2014 at 11:19 | comment | added | Dinesh | @MartinHairer, thank you very much for your remark. That was a mistake, sorry. I am in fact looking at the integral to $T_{sup}(F)=\sup_{\{M\in\frak{M}\}}\{\int_{[\alpha,1-\alpha]}F^{-1}(s)M(ds)\}$ for $\alpha>0$ | |
| Nov 26, 2014 at 11:17 | history | edited | Dinesh | CC BY-SA 3.0 |
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| Nov 26, 2014 at 10:39 | comment | added | Martin Hairer | You'll certainly need some additional assumptions since $F^{-1}$ typically diverges near $0$ and $1$, so that $T$ can easily be infinite. This is extremely unstable under weak convergence of the CDF $F$, so that $T$ cannot be continuous if $M$ has support at $0$ or at $1$. | |
| Nov 26, 2014 at 2:36 | history | edited | Dinesh | CC BY-SA 3.0 |
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| Nov 26, 2014 at 2:35 | comment | added | Dinesh | @MartinHairer, yes, sorry. I mean CDF. And, also, yes, weak convergence. | |
| Nov 25, 2014 at 21:48 | comment | added | Martin Hairer | When you say that the domain are 'random variables', do you mean 'cumulative distribution functions'? What topology do you want on these? (Presumably weak convergence for the corresponding probability measures?) | |
| Nov 25, 2014 at 16:05 | comment | added | Dinesh | @JochenWengenroth, Sorry, I avoided details as I thought the details might not effect the result. I have added details if that can help. | |
| Nov 25, 2014 at 16:03 | history | edited | Dinesh | CC BY-SA 3.0 |
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| Nov 25, 2014 at 15:05 | comment | added | Jochen Wengenroth | The question is not clear. What is the domain of $T$? Do you mean by $F^{-1}(s)$ the multiplicative inverse $1/F(s)$? | |
| Nov 25, 2014 at 13:16 | review | First posts | |||
| Nov 25, 2014 at 13:25 | |||||
| Nov 25, 2014 at 13:14 | history | asked | Dinesh | CC BY-SA 3.0 |