Timeline for Expectation of random integral of deterministic function
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Feb 6, 2017 at 13:51 | comment | added | Sasho Nikolov | Let me be more explicit: your equality will not hold in general, and examples are abundant. For example take $f(t) = 2t$. In that case you are asking if $\mathbb{E}[W^2] = \mathbb{E}[W]^2$, which holds if and only if $W$ has variance 0. In general, I expect that the only continuous $f$ for which your equality holds are constant on the range of $W$. | |
| Feb 6, 2017 at 10:39 | comment | added | Liäm | Yes, that's what I mean basically, but I, in fact, did not come up with your representation. I have not tried any function yet, but my case will be continuous and differentiable functions with $\inf\{s > 0 : f(s) > 0\}$. | |
| Feb 6, 2017 at 6:56 | answer | added | JGWang | timeline score: 1 | |
| Feb 6, 2017 at 6:35 | comment | added | Sasho Nikolov | Did you try with any function $f$? You are basically asking when $\mathbb{E}[F(W)] = F(\mathbb{E[W]})$ for a differentiable function $F$. | |
| Feb 6, 2017 at 6:03 | review | First posts | |||
| Feb 6, 2017 at 6:04 | |||||
| Feb 6, 2017 at 5:59 | history | asked | Liäm | CC BY-SA 3.0 |