Talk:Wiener process

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I erased the reference to random walk, since it was imprecise and the information about the variance of the Wiener process was yet stated above. I added some words about the role of the Wiener process in Pure and Applied Mathematics. Gala.martin 20:27, 6 February 2006 (UTC)

The picture previously showed a Brownian bridge, not a general Wiener process. Although a simulation of a Wiener process might turn out to look like a Brownian bridge by pure chance, I think it is preferrable to use another picture here, so I changed it. --PeR 12:20, 30 June 2006 (UTC)


I think that we had better put R(s, t)=E[X(s)X(t)]=sigama squre*min(s,t)

covaviance gamma(s,t)=E[(X(s)-m(s))(X(t)-m(t))]=...

and its derivative.

a=t0<t1<...<tn=b

Limit of the Sum [W(tk)-W(t(k-1))]^2 = b-a

(I)\int_{a}^{b} W(t)\,dW(t) = (W^2(b)-W^2(a))/2-(b-a)/2.
(S)\int_{a}^{b} W(t)\,dW(t) = (W^2(b)-W^2(a))/2.
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