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Let $X_o=x$, $dX_t=\frac{1}{X_t}dt+X_tdW_t$, $W_t$ is a brownian motion i am thinking of trying $Y_t=\frac{X_t^2}{2}$ and apply ito's lemma on $Y_t$

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    i think $Y_t=\frac{-X^2_t}{4}$ will do the trick2011-11-08
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    As a solution of what?2011-11-08
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    i mean trying $Y_t$ , and then apply ito's lemma on $Y_t$ and find $X_t$2011-11-08
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    You might wish to reconsider: solving an equation usually means expressing the unknown as an explicit function of the given, here the unknown is X and the given is W so you cannot express a solution as a function of X.2011-11-08
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    $W_t$ is brownian motion2011-11-08
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    Hmmm... in fact $(W_t)_{t\geqslant0}$ is a Brownian motion, $W_t$ is just a random variable. But I wonder what this has to do with my remark.2011-11-08
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    Do you mean that you're trying to guess the solution?2011-11-08

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