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 $Y_t$
Solution to the stochastic differential equation
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probability-theory
stochastic-processes
stochastic-integrals
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0i think $Y_t=\frac{-X^2_t}{4}$ will do the trick – 2011-11-08
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0As a solution of what? – 2011-11-08
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0i mean trying $Y_t$ , and then apply ito's lemma on $Y_t$ and find $X_t$ – 2011-11-08
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0You 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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0$W_t$ is brownian motion – 2011-11-08
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0Hmmm... 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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0Do you mean that you're trying to guess the solution? – 2011-11-08