$$dX_t = -\frac{1}{2}e^{-2X_t}\ \ dt+e^{-X_t}dB_t, X_0=x_0$$
Hint: solve this equation using the substitution $X_t=u(B_t)$, show that the solution blows up at a finite random time.
$$dX_t = -\frac{1}{2}e^{-2X_t}\ \ dt+e^{-X_t}dB_t, X_0=x_0$$
Hint: solve this equation using the substitution $X_t=u(B_t)$, show that the solution blows up at a finite random time.