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we are wondering what can be said about the distribution of that? We are considering standard Brownian motions and the integral from 0 to 1... More precisely: What can be said about the distribution of $$\int_0^1 W^\epsilon_u dW^\eta_u$$ where $W^\epsilon$ and $W^\eta$ are independent standard Brownian motions. It certainly has mean zero but I don't quite know how I could do anything else with that...

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Please ask a more specific question, otherwise there is not much to say. –  Dan Brumleve Nov 25 '12 at 12:05
    
And please include fully the question in the body instead of relegating it to the title. –  Did Nov 25 '12 at 12:07
    
Sorry I hope it is clearer now –  Oliver Nov 25 '12 at 15:22
    
Centered normal with variance 1/2. –  Did Nov 25 '12 at 15:33
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thank you did, could you give me a hint on how you arrive there? –  Oliver Nov 25 '12 at 15:45
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