Talk:Itô calculus

message: This should say who Ito is. Michael Hardy 22:31, 15 Mar 2005 (UTC)
replies: text: Why? If you want to know, read the link to his bio. --Prosfilaes 03:08, 30 July 2005 (UTC)
thread_title: Who is Ito?

message: Should it be Itō Calculus or Itô Calculus? The article should be consistent in the math terminology, which I'm sure most math articles are, and not necessarily consistent to the name of the author. It's more important that it be consistent to modern math usage, then one arbitrary translation of the creator's name, IMO. --Prosfilaes 03:08, 30 July 2005 (UTC)
replies: text: The proper way I have seen his name written has been Itô. I am uncertain where this 'ō' came from, but I have only seen it used in the Wiki text. Mdbrack 07:36, 20 April 2007 (UTC)

text: Neither is "proper", and neither is "wrong". They are simply two different romanizations of the same Japanese name, 伊藤 清. This is treated both on Itō's biographical page and pages on the Hepburn romanization, from which the following line might be helpful to you: "Circumflexes are how long vowels are indicated by the alternative Nihon-shiki and Kunrei-shiki romanizations [as opposed to macrons in standard Hepburn]. Circumflexes are often used when a word processor does not allow macrons. With the spread of Unicode, this is becoming rare." Sullivan.t.j 15:06, 20 April 2007 (UTC)

text: I just checked on MathSciNet. Pretty much all of his articles are signed "Kiyosi Itô", except for those written in the eighties that are signed "Kiyosi Itō". Some of them are signed "Kiyoshi Itô" but again, it is a minority. By that time, every editor would have been able to typeset "Itō" if this is what he wanted. I conclude that either Itô didn't have much of an opinion on how to romanize his name, or he actually preferred "Kiyosi Itô", whatever the standard romanization. Since "Kiyosi Itô" is also the romanization used in various prominent locations (see http://www.ams.org/notices/199808/comm-kyoto.pdf or http://www.kurims.kyoto-u.ac.jp/~kenkyubu/past-director/ito/ito-kiyosi.html), I propose to change the name back to "Itô". Hairer (talk) 13:06, 15 September 2010 (UTC)

text: I spoke to a number of people who knew Itô personally. They all agreed that the way he wanted his name to be spelled is "Kiyosi Itô". As a matter of fact, he was apparently quite upset when people spelled his name as "Kiyoshi Itô" or "Kiyoshi Itō". I believe that ultimately the bearer of a name gets to decide what the "correct" spelling of that name is, so I will revert to his preferred spelling if there is no objection. Hairer (talk) 01:39, 11 September 2015 (UTC)
thread_title: Itō or Itô

message: The causality of Itō Calculus should be emphasized linguistically, not just stated mathematically.  I'd do it, but Stochastic calculus was my worst subject in my twenty-odd years of schooling., so perhaps someone less likely to introduce imperfections could do this. Calbaer 20:57, 10 March 2006 (UTC)
thread_title:  Causality 

message: I added this section, and removed the old section "Generalization: integration with respect to a martingale" as it didn't make much sense, was full of mistakes, and is covered by the new section now.Roboquant (talk) 02:04, 7 March 2008 (UTC)
thread_title:  Integration With Respect to Semimartingales 

message: I added the maths rating template, rating it as High importance. Ito calculus is certainly very important to probability and statistics, but is also very important outside of maths. It is widely used in finance, and is fundamental to the theory of option pricing (e.g. Black-Scholes). It is also important to stochastic differential equations, areas of physics and in engineering (eg filtering). I propose increasing it to Top. Any comments?  —Preceding unsigned comment added by Roboquant (talk • contribs) 22:22, 22 March 2008 (UTC)
thread_title:  Rating 

message: The term is popularly referred to as Ito. As of 2008-04-24, Google returns 32,600 hits for "Ito calculus" -wikipedia. For reasons of simplicity, I recommend that this page be moved to Ito calculus. There is no good reason to use a non-standard character; it needlessly fragments search results. Please vote in favor of or against the move, along with your reasons. --AB (talk) 21:16, 24 April 2008 (UTC)
thread_title:  Page move request to "Ito calculus" 

message: As it is, this article is nicely written for mathematicians but hardly readable for physicists.
This is really a sad state of affairs, since the same is true for most math textbooks on stochastic calculus.
I would love to read here something in more familiar notation, e.g.
In physics, usually stochastic differential equations are used instead of stochastic integrals.
A physicist would formulate an Ito stochastic differential equation (sde) as
: \dot{x}_k=h_k+g_{kl} \xi_l
where \xi_j is Gaussian white noise with \langle\xi_k(t_1)\,\xi_l(t_2)\rangle=\delta_{kl}\delta(t_1-t_2)
and Einstein summation convention is used.
If y=y(x_k) is a function of the  x_k , then the Ito chain rule has to be used
: \dot{y}=\frac{\partial y}{\partial x_j}\dot{x}_j+\frac{1}{2}\frac{\partial^2 y}{\partial x_k \partial x_l} g_{km}g_{ml} 
An Ito sde as above corresponds to a Stratonovich sde which reads
: \dot{x}_k = h_k + g_{kl} \xi_l - \frac{1}{2} \frac{\partial g_{kl}}{x_m} g_{ml}
Stratonovich sde frequently occur in physics as the limit of a stochastic differential equation with colored noise
if the correlation time of the noise term approaches zero.
For a recent treatment of different interpretations of stochastic differential equations see for example 
Lau, Lubensky: State-dependent diffusion, Phys. Rev. E, 2007.
--Benjamin.friedrich (talk) 09:45, 28 August 2008 (UTC)
thread_title:  Make this article available to physicists 

message: I might be mistaken, but does not the infinite variation only hold almost surely ?  —Preceding unsigned comment added by 129.240.176.119 (talk) 12:11, 5 April 2009 (UTC)
thread_title: Errors

message: I'm a professional mathematician (albeit an algebraist), and I find this article incomprehensible.  It suffers from the same shortcomings as many other technical articles on Wikipedia:  It doesn't explain its terminology (which certainly does not belong to the mathematical mainstream), it doesn't motivate, it provides too few examples.  I'm not competent to improve it, but it would be worth for someone who is to rewrite it.  —Preceding unsigned comment added by 128.240.229.65 (talk) 17:06, 27 October 2008 (UTC)
thread_title: This article is incomprehensible

message: This chapter suddenly introduces a new notation In general, the stochastic integral H  ·  X can be defined even in cases where the predictable process H is not locally bounded., which is used in the next chapters, without giving a proper definition. IS this the same as \int_0^t H\,dX? Albmont (talk) 14:55, 12 August 2009 (UTC)
thread_title:  Semimartingales as integrators 

message: I have added a clarify tag (put it back again) because the notation here is still unexplained. If the article quadratic variation is supposed to be supplying this inforamtion it fails to do so as it uses a different notation (square brackets rather than angle). Melcombe (talk) 09:51, 18 February 2010 (UTC)
thread_title:  Further extensions section 

message: The 5-tuple characterizing a filtered probability space has missing or inadequate descriptions, but the underlying article also does not provide these descriptions. Vonkje (talk) 19:04, 18 November 2010 (UTC)
thread_title:  Formula missing descriptions 

message: This section is poorly-written and needs to be revamped.  The differentiation theory has to be stated correctly with proper citation. AaronKauf (talk) 18:24, 29 August 2011 (UTC)
replies: text: I am actually in favour of having that whole section removed. As stated below a number of single-purpose accounts, of which RHarryd is the latest, have tried to add exactly the same material over the years. As explained on this talk page by regular watchers/editors of this page, the present version was a compromise to stop the constant addition of WP:UNDUE material on what is claimed to be "Allouba theory" and make the article stable. If AaronKauf, another recently arrived user, could tone down his language and assume good faith, that would be helpful. Mathsci (talk) 06:15, 11 September 2011 (UTC)
replies: text:  Mathsci: the assumption of good faith cannot be maintained when your statements and actions clearly point to a different conclusion.  Let's be honest for a change, the current version is not a compromise.  The compromise was one that included both mart rep theorem and Allouba's theory (it's not "claimed theory" and it's hard to respect your opinion when you keep disrespecting the established facts in respectable journals).  It is most certainly Allouba's differentiation theory, it is a complete rigorous counterpart to Ito's integral calculus that in and of itself is quite notable given the long history of Ito calculus without such a differentiation theory (the quite notable Malliavin derivative is in the Gaussian not Ito's semimartingale setting).   It has also led to, among other things, a version of the Clark-Ocone formula (one of the important applications of Malliavin derivative) that compares favorably in applicability and simplicity to the very notable Malliavin derivative version (this paper is already accepted and to appear and available on arXiv).  So, stop with the disingenuous smart Alec comments.   Several of us have addressed Mathscinet references regarding top mathematicians and their important work with very few citations over a long period, so that argument falls on its face.  AaronKauf is absolutely right on, this is transparently personal or some other equally ugly reason or worse (this becomes clear when you are advocating the removal of Allouba's work but you're happy with a mart rep theorem section that doesn't have any differentiation theory in it, it is  completely non rigorous and not complete as far as differentiation is concerned, and the added references are not differentiation references).  Labeling AaronKauf "another recently arrived user" and everybody who disagrees with you a "spammer" or a "single purpose account" in an obvious attempt to discount their opinion doesn't earn you respect.  Coordinating with others so that as soon as someone posts a version containing all the facts, including Allouba's theory, you (or they) delete it before giving the rest time to even see it is the definition of bullying.  Everybody, single or multi purpose has the right to give their input and for that input to be respected.  It is not up to you or Hairer or the rest of the posse to decide what established facts should be removed so that their author doesn't receive additional notoriety (an obviously personal motive).  You are entitled to your own opinions but you're not entitled to your own facts.  You and the posse are not entitled to selectively hiding anybody's well established verifiable work, in a respectable journal, even if you don't like it.  This is a global encyclopedia not your book, it should contain all the relevant mathematical facts not just the ones you like.   A section about "differentiation in Ito calculus" without Allouba's quadratic covariation differentiation theory is not an honest description of that now-part of Ito's calculus.  Removing the differentiation section from any calculus when it exists is not appropriate either. This behavior is not tolerated in Wikipedia.RHarryd (talk) 23:29, 11 September 2011 (UTC)
replies: text: Your account has been single-purpose so far like the others described below; it is indistinguishable from those previous accounts. Again this content has not yet been recognized as notable as can be gauged from mathscinet and its non-inclusion in academic textbooks. There is a huge literature on the Ito calculus. The wikipedia article can only represent what has been assimilated and already recognized in the academic literature, in this case academic textbooks. All the material that has appeared in the section on differentiation, including the current content, is WP:UNDUE or WP:OR. There is a huge literature on the Ito calculus and it is not wikipedia's role to record all the content from individual papers. Wikipedia uses academic textbooks as the main sources in this particular context. On wikipedia personal opinions of editors on the merits of individual contributions are irrelevant, as we can only go by what secondary sources say, in this case academic textbooks. Personal opinions, as far as wikipedia is concerned, are just WP:OR and WP:SYNTH. Please see WP:NOTCRYSTALBALL. Making a comparison between Allouba and Fields medallists is also not particularly helpful. Thanks, Mathsci (talk) 04:53, 12 September 2011 (UTC)

text: I have restored the Allouba QCD section as it is inseparable from the differentiation section, and should never be removed.  I have retained the Malliavin derivative section, even though it has its own page and even though the Malliavin calculus is a Gaussian calculus not Ito calculus.  The section on the mart rep thm is not mathematics as it was:  one cannot just say we can "formally" interpret something as a derivative without giving at least a reference to a rigorous treatment of this assertion or relate it to a rigorous treatment.  The Williams reference is not enough since it does not give the differentiation theory.RHarryd (talk) 15:14, 22 September 2011 (UTC)
replies: text: The arguments for not having this material have not changed and will not be repeated. Mathsci (talk) 16:14, 22 September 2011 (UTC)
replies: text:  What is your mathematical basis?  Having a personal issue with the author, is not a mathematical argument. AaronKauf (talk) 16:18, 22 September 2011 (UTC)
replies: text: The mathematical notability of the work of Alouba has been already explained above. Both RHarryd and AaronKauf are WP:SPAs whose sole contributions to wikipedia have been to add content related to Allouba theory, which has not yet been recognized as being significant within mathematics. Edit warring to include this unnotable content could result in a report at WP:ANI. I would advise both of you to ask for input from WikiProject Mathematics. Attempts to insert this material have been going on for a number of years and very little has changed regarding the reception of this material within mathematics. The importance of the material is gauged from secondary sources and from mathscinet. Comparisons to the reception of work by Fields medallists so far have been without any merit whatsoever. Mathsci (talk) 16:41, 22 September 2011 (UTC)
replies: text:  Please read the above comments before issuing your regular veto. This behavior of vetoing and threatening is unethical and based on unsubstantiated claims.  Your account along with the other British ones are WP:SPAs.  AaronKauf (talk) 17:22, 22 September 2011 (UTC)
replies: text:  Why are you even bothering to say that? We all know how to press the "contributions" tab, and we're not stupid. You are the SPA, that is painfully obvious William M. Connolley (talk) 21:57, 22 September 2011 (UTC)
replies: text:  Why are you (along with Mathsci) enticing an edit war by constantly reverting and deleting any contribution we do to this section?  You are not even willing to engage in a constructive mathematical discussion.  It is obvious that you and your group are having personal issues with the author Allouba.  And as I stated before, the Wiki is not a vehicle to settle scores.  The constant harassment and threats issued by you and your friends are unethical, and against Wiki policies; and are being reported.  AaronKauf (talk) 02:19, 23 September 2011 (UTC)
replies: text:  I know nothing of Allouba; you are completely wrong to think I am trying to settle some non-existent "score". There has been no harassment, and no threats William M. Connolley (talk) 20:57, 29 September 2011 (UTC)
replies: text:  Well, it's true that Hairer is the one who brought up this author and shifted a mathematical discussion into a personal one, but you followed suit.  Why resort to the personal attacks instead of solving a mathematical issue? AaronKauf (talk) 17:06, 1 October 2011 (UTC)
replies: text:  I'm not sure this discussion is going to work very well. You started with Your account along with the other British ones are WP:SPAs which is quite wrong, indeed a PA, a a glance at our contributions will show; conversely you are an SPA; you continued by argument from spurious authority. Meanwhile, on your talk page you've been informed of a proposal to ban you indefinitely, for the reasons given here . It really would be a good idea for you to respond there; a completely uninvolved admin has said of you Reasoning with this editor does no good. He won't respond at ANI, but continues to make warlike statements on article talk pages. He takes the interesting view that he doesn't need to give his real name (we should trust him as an authority) but he criticizes other editors for not giving their real names. Since he really won't listen, an indef block is appropriate William M. Connolley (talk) 18:03, 1 October 2011 (UTC)

text:  Again, let's be clear on this. I have nothing personal against Allouba and I have no idea where you got that idea from. Also, I know neither William M. Connolley nor Mathsci and, again, I have no idea where you got the idea that I am somehow hoarding a bunch of friends to run after you and / or Allouba. Hairer (talk) 18:20, 1 October 2011 (UTC)
thread_title:  Differentiation in Itō calculus 

message: Is there (open-source) software available which integrates Itō stochastic differential equations? References to this software and perhaps applications would be really valuable. Andy (talk) 08:20, 25 August 2011 (UTC)
thread_title:  Software / libraries 

message: I'm hereby invoking WP:BURDEN  and WP:CHALLENGE on the entire article.  I've read through it, and the total lack of citations is not compliant with the WP:Verifiability policy, given that I'm challenging the material, and given the existence of an RfC questioning key parts of the article.   In accordance with Wikipedia:Scientific citation guidelines, a single citation per paragraph may be acceptable, provided that the source does indeed cover the entirety of the paragraph it is supporting.  (PS:  I originally made this comment above in the RfC section, but Im repeating it here to be more prominent). --Noleander (talk) 03:19, 10 September 2011 (UTC)
thread_title: Citations needed:  see [[WP:BURDEN]] 

message: Neither is mentioned, yet a link ftom the Ito's Lemma page says "Assume X_t is a a Itô drift-diffusion process that..." and links here, but drift is not mentioned. Could someone make this explicit?  — Preceding unsigned comment added by 193.52.24.38 (talk) 08:44, 5 June 2016 (UTC)
thread_title:  Drift and Diffusion 

message: This whole section looks more like an attempt at self-promotion than anything else to me. This perspective on SDEs is certainly not mainstream and does not really seem to bring anything new from a mathematical perspective. The main point seems to be to promote the "superiority" of the Stratonovich interpretation of SDEs over their Itô interpretation, which is simply not a mathematical question. The fact that the main (and very long) article as well as the addition on this page were entirely created by a single account operating under an obviously fake name certainly raises red flags... Hairer (talk) 21:18, 5 June 2017 (UTC)
thread_title:  Supersymmetric theory of SDEs 

message: How can there be a whole article on the Itô integral that does not mention the notion of progressively measurable? Isn't that the weakest class of processes that can be integrated against a given semimartingale? 
It seems that the article uses adapted processes and then (sometimes) supplements them to be cadlag, which implies that they are progressively measurable, but this is not mentioned, instead the discussion goes straight to the Itô integral.
If I am mistaken on this point, then there is an error in the article Progressively measurable processes, subsection Properties, which asserts what I've said here. 
I found the following chain of inclusions to be helpful in keeping these classes straight:
:(Continuous + adapted) -> (mean-square continuous + adapted) -> predictable -> optional -> progressive -> adapted.
where all these classes are understood to be subsets of L^2(Omega x [0,T]).
I hope this chain of implications is correct; it came from stackexchange.
2A02:1210:2642:4A00:2C0E:9FB8:44BB:17B6 (talk) 12:37, 4 November 2023 (UTC)
thread_title:  Progressively measurable