{\rm d}y &=& \frac{1}{x}{\rm d}x - \frac{1}{2x^2} ({\rm d}x)^2\\
 &=& \frac{1}{x}(\mu x {\rm d}t + \sigma x {\rm d}W_t) - \frac{1}{2x^2}(\sigma^2 x^2 {\rm d}t)\\
 &=& (\mu - \frac{1}{2}\sigma^2){\rm d}t + \sigma {\rm d}W_t
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