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I am trying to do the following stochastic integral

$$ \int_0^T \mu(B_s) dB_s - \frac{\int_0^T (\mu(B_s))^2 ds}{2} $$ where $ \{ B_t \}$ is a standard Brownian motion, and $\mu(x) = \frac{\beta}{2x} (x^2 - \frac{4\gamma}{\sigma^2} - \frac{1}{ \beta})$.

I currently only know how to integrate when the integrands are constant, i.e. $\mu$.is constant function. I was wondering how to integrate under more complicated case as above.

Thanks and regards!

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    Is that a $\sqrt{x}$ in the denominator? What do you want it to do when $x=B_s$ is negative?2010-11-20
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    @Nate: Sorry, I made a mistake when deriving this expression. I just made the correction to the post.2010-11-23
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    How do you define *to compute*? Is it: to express as a function of $B_0$, $B_T$ and $T$?2011-03-17
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    @Didier: Yes, I think so. It has been a while, and I am still learning towards solving similar kinds of problems. .2011-03-17
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    My point is that it is not always possible to get rid of every integral term--as answers by @Sivaram and @TheBridge basically show. So what you can get are several equivalent expressions for your Brownian functional, none of which actually *computes* it.2011-03-17

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