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 $$X, Y \in L^2_{\mathrm{ad}} ([0,T] \times \Omega)$$ .138.246.2.189 (talk) 12:44, 17 May 2018 (UTC)kw