Talk:Itô isometry

-Not consequent, in some wiki-articles the BM is denoted Brownian Motion with B or X and in this one (linked from such an article) we have Wiener process W. Not saying one is better than the other but decide on one

-"...of variances for RANDOM VARIABLES" would be more appropriate, since T is fixed. W being a F-Brownian should be enough, no need for F to be the natural filtration.

the explanation "why is it an isometry"

The norm on L^2(W) should be define as the integral on [0;T] of the expectation, because here the isometry presented is trivial, and doesn't use the isometry formula... — Preceding unsigned comment added by 46.193.0.25 (talk) 17:56, 6 June 2016 (UTC)

I've fixed it. Hairer (talk) 14:42, 10 June 2016 (UTC)

Missing Citation

In the book of Oksendal it is not mentioned that :$\mathbb {E} \left[\left(\int _{0}^{T}X_{t}\,\mathrm {d} W_{t}\right)\left(\int _{0}^{T}Y_{t}\,\mathrm {d} W_{t}\right)\right]=\mathbb {E} \left[\int _{0}^{T}X_{t}Y_{t}\,\mathrm {d} t\right]$ for $X,Y\in L_{\mathrm {ad} }^{2}([0,T]\times \Omega )$ .138.246.2.189 (talk) 12:44, 17 May 2018 (UTC)kw