Talk:Adapted process

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Interpreting "Adaptiveness" as that such a process "not being able to look into the future" seems at least odd, as at first sight the measurability properties seem like a positive property("the filtration contains at least the history of the process") and not a negative one (not being able to look into the futures, such interpration i find to be more plausible for the negation of "predictability" as for example according to the Wikipedia Page on "Predictable Process"). Along these line I expect the existence of an adaptive "but" also predictable process (contradicting the interpretation in the article). Am I way off here ?

Adapted process is related to "predictable process"/"nonanticipating process"? Jackzhp 06:01, 1 September 2006 (UTC)Reply

Yes, "adapted" and "non-anticipating" are synonyms. I have added a note to this effect in the main article. I have also added redirects from "nonanticipating process" and "non-anticipating process". Sullivan.t.j 22:37, 1 September 2006 (UTC)Reply

Are you sure? I think we can have a process that is not adapted, but still non-anticipating. For example, if F is filtration generated by Brownian motion, and G is filtration that contains F plus extra, but this extra is independent of the future, then we can define a process X(t) that is NOT adapted to F (depends on this extra), but is still non-anticipating. You can actually integrate this process w.r.t Brownian motion, but Ito/Martingale representation will not work (I think). 89.235.241.7 (talk) 22:50, 26 May 2011 (UTC)Reply

"Integrand"? when I clicked it, I was directed to Integral. Is there anything wrong here? Jackzhp 05:03, 1 September 2006 (UTC)Reply

No, nothing is wrong. If you read the article Integral, you will see that the term "integrand" is defined: it is the thing that is integrated. Sullivan.t.j 22:37, 1 September 2006 (UTC)Reply

It seems that some processes can see into the future, some can not. Can someone please give an example for each case? Jackzhp 05:05, 1 September 2006 (UTC)Reply

Done. :-) Sullivan.t.j 22:37, 1 September 2006 (UTC)Reply

When you get a moment, could you glance at this edit to see if it's ok? I don't have the knowledge to judge. Joyous! Noise! 03:34, 7 May 2025 (UTC)Reply

That's me, I made that edit. It's fine. You can find a definition of fineness (and coarseness) in Comparison of topologies and in Fine topology. Here, we're dealing with sigma algebras and not topologies, but the same general idea applies. 67.198.37.16 (talk) 23:56, 9 May 2025 (UTC)Reply