Talk:Itō's lemma
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Is anyone who knows what they are doing, re: Wiki, still monitoring this page? I note that Pcb21/Pete seems to have taken a break from Wiki.
In any case, (a) it is incorrect to state Itō's Lemma in "differential form" as is done in this article (and just about everywhere else that the Lemma is "stated") -- the equality holds for the integral, but not for the differential "equivalent;" (b) I can provide a formal proof (my own), if someone is willing to verify it, but I am completely unfamiliar with the math editor here. --Marsden 23:52, 23 August 2005 (UTC)
The differential and integral form are exactly equivalent. What makes you think they differ?
I've recently written up a formal proof to Ito's lemma if anyone wants it.
- Wikipedia itself would greatly benefit from such a proof. Would you be willing to release under our free licence? If you don't want to spend the time converting from what format you have it in to wiki-markup you could send it to me and I could do it. Let me know! Thanks for your interest Pete/Pcb21 (talk) 08:52, 11 Feb 2004 (UTC)
Shouldn't it be "Itô's lemma" with the appropriate accent mark? I think "Ito's lemma" (without the accent) was the cause of O.J. Simpson's acquittal or something? --Christofurio 15:36, Apr 12, 2004 (UTC)
- moved, kept redirect. If something is written about the OJ case, we would need to re-think the names to minimize confusion. Pete/Pcb21 (talk) 20:41, 12 Apr 2004 (UTC)
- What is with the ô? It's a Japanese name and in Romaji, o is o; there is no ô. Is it an Ainu name?
What does the formal proof require? We say it needs different things in two different places... can we rationalize/improve on this? Pete/Pcb21 (talk) 23:32, 15 Apr 2004 (UTC)
I think this "proof" should not really appear on the page, since the Taylor serie does not always exist, that we can't really reorder the terms of the expansion, and finally that the error term may not be negligeable. And finally, this proof does not give the intuition of why the Ito's lemma is true.. 140.247.43.68 20:23, 19 March 2006 (UTC)
i'm interested in this and other stochastic calc stuff for financial applications, but my background is only differential and integral calculus (called I and II usually), and that was years ago. can someone, please, explain what ito's lemma does or means just in english, without any mathematical symbols? that would be very helpful. thanks guys.
this probably applies to darn near all the math pages, i think. it makes it usable for more people if it has an english-only description (could be even 1 sentence) somewhere in there, preferably at the beginning.
i know you guys are very good with math but some of us plebeians are lost by this sort of notation. :) thanks guys.
- The differential of a function is a linear approximation of the change in the function. That is, the graph of the function is approximated by a straight line or a plane. If f is a function of t and W, then its differential df is a linear function of dt and dW that is approximately equal to the change in f. The differential df is calculated from the actual change by ignoring higher-order terms, e.g. squares and cubes. However, in stochastic calculus dW^2 is not really a higher-order term, and so it cannot be ignored. The order of dW is really one half so that the order of dW^2 is one; in fact dW^2 is equal to dt. The usual formula for the differential of a function has to be modified to take this into account, and this is what Ito's lemma does.—Zophar 15:59, 20 November 2006 (UTC)
