Talk:Stochastic differential equation
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Created a new page here from what was previously all in Langevin equation - which is actually more specific than just an SDE. More work is needed. --SgtThroat 15:04, 4 Jan 2005 (UTC)
I don't get it: "A weak solution consists of a probability space and a process that satisfies the integral equation, while a strong solution is a process that satisfies the equation and is defined on a given probability space."
I read this to say that a weak solution satisfies A&B, while a strong solution satisfies B&A. Please clarify.
[edit] Terminology?
The terminology subsection currently says that SDEs can be written in one of three forms, the third of which is "as an SDE". Could someone clarify that?
Also, under "use in physics", it says that the noise is multiplicative if gi(x) is not constant. Isn't it only multiplicative if 
? LachlanA (talk) 05:29, 15 January 2008 (UTC)
[edit] weak vs strong solution, a typo
I think the formulation in the text is correct and slightly different from what you quoted, namely ``... strong solution ... in the given probability measure". Where ``the" refers to the given probability measure of the SDE. This requires especially that the solution process Xt is defined for all elementary events ω. While for a weak solution you can first restrict the probability measure (and especially its underlying sigma-algebra) to a convenient subspace (possibly rescaling the prob-measure).
Towards the end of the current article I guess there is a typo in the formulation of the Ito-SDE. Namely you should not set equal the process Xt (for all t) to the random variable Z. It would make sense if you wrote X0 = Z. Before I change this I'd prefer someone had a look in one of the literature sources and check if that is correct.
[melli]64.178.100.37 (talk) 04:10, 16 March 2008 (UTC)
[edit] History of SDE
This is the first time I am making a posting. I may not be doing this the best way possible.
The article correctly cites Bachelier (1900) as one who wrote the stochatic DE before Enstein.
It turns out that prior to Bachelier, Edgeworth (1883) and Lord Rayleigh (1880, 1894)
Edgeworth, F.Y., The law of error, Phil. Mag., Fifth ser., 16, 300-309, 1883.
Rayleigh, Lord, On the resultant of a large number of vibrations of the same pitch and of arbitrary phase, Phil. Mag., 10, 73-78, 1880.
Rayleigh, Lord, The Theory of Sound, MacMillan and Co., London, Vol. 1, Second Edition, 1894.
Historical details can be found in,
Narasimhan, T. N., Fourier's Heat Conduction Equation: History, Influence, And Connections, Reviews of Geophysics, 37(1), 151-172, 1999
Narasimhan —Preceding unsigned comment added by Tnnarasimhan (talk • contribs) 23:30, 3 May 2008 (UTC)
