Given is the stochastic differential equation:
$\frac{dX(t)}{X(t)}=\mu+\sigma \theta dt+ \sigma dW(t)$, where $W(t)$ is the standard Wiener process and $X(0)=x_0$
I try to solve this by the Itos formula by setting $f=log(X(t))$ and then taking the Itos differential:
$d log (X(t)) = \frac{1}{X(t)}dX(t)-\frac{1}{2 X(t)^2}dX(t)^2$.
Im wondering if this is the right way to go? Since I know that this will be a messy calculation in that case. Also, the constant $\mu$, how should I look at it when integrating on both sides?
Thank you
Thank you