How to solve $\mathrm dX(t)=X(t)^2 \mathrm dt+X(t)\mathrm dB(t)$ with condition $X(0)=1$?

I want to solve the stochastic differential equation $$\mathrm dX(t)=X(t)^2 \mathrm dt+X(t)\mathrm dB(t)$$ with condition $X(0)=1$.

• Should this be on the math site or here? – Peter Flom Jan 1 '14 at 14:35
• @PeterFlom, the question asks about a stochastic differential equation (probability theory), so it's on-topic here (and also on math.SE). – cardinal Jan 1 '14 at 14:54
• Hint: Analyze $Y_t = e^{-B_t + \frac12 t} X_t$. – cardinal Jan 1 '14 at 23:42
• Also posted on MSE (also without explanations of any kind), where it got an (accepted) answer explaining two different approaches. This could be closed. – Did Jan 2 '14 at 12:41
• @Did hello, and this is slightly different to the math.se question, i think. But i agree prob should be closed. – Lost1 Jan 2 '14 at 13:06