This article is within the scope of WikiProject Statistics, a collaborative effort to improve the coverage of statistics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.StatisticsWikipedia:WikiProject StatisticsTemplate:WikiProject StatisticsStatistics articles
This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.MathematicsWikipedia:WikiProject MathematicsTemplate:WikiProject Mathematicsmathematics articles
-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 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)[reply]
I've fixed it. Hairer (talk) 14:42, 10 June 2016 (UTC)[reply]
![{\displaystyle \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]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/20f844d3603c93d0bc1ac91184c1cbcc3aa9aba0)
![{\displaystyle X,Y\in L_{\mathrm {ad} }^{2}([0,T]\times \Omega )}](https://wikimedia.org/api/rest_v1/media/math/render/svg/048aded9590cd42ded3599a3e577c6fb33adb90b)