Say we have $X_t$ and $Y_t$ are stochastic processes and $f$ is a differentiable function.
If we have:
$\displaystyle dX_t = (rdt+adB_t)X_t,\text{ where } B_t$ is (standard) Brownian motion
then we end up with Geometric Brownian motion.
I want to consider the following:
$\displaystyle dX_t = -f(X_t)Y_t(dt+dB_t)$
and let us assume $Y_t$ is a process driven by Brownian motion.
Can this be solved for in a similar way as the Geometric Brownian motion case?