Timeline for What does progressively measurable actually entail?
Current License: CC BY-SA 3.0
4 events
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| Apr 20, 2011 at 8:09 | vote | accept | Jerry | ||
| Apr 20, 2011 at 8:09 | comment | added | Jerry |
Okay, in establishing measurability of $\phi$, I was getting confused by trivialities that I shouldn't have. (I actually did pass the comprehensive exam on measure theory and analysis in grad school :-) I'm accepting your answer for pointing out the fact about $t \mapsto f(t, X_t)$. I'll take it that that's important for things like Itô's formula. Details like that are often passed over in the texts that I've been reading.
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| Apr 19, 2011 at 20:26 | comment | added | weakstar | In particular, for $\theta_t(\omega)$ progressively measurable, $\theta_T \in \mathcal{F}_T$ when $T$ is an arbitrary stopping time. If $\theta$ is just adapted, this will only hold true when $T$ is countably valued. I think an ok analogy is progressively measurable is to adapted as strong markov is to markov. | |
| Apr 19, 2011 at 18:24 | history | answered | BSteinhurst | CC BY-SA 3.0 |