If I have a stochastic differential equation in the following form: $$ \frac{dx}{dt} = \frac{A}{B+\sigma_1\Gamma_1}(\sigma_2\Gamma_2 \sin x+\sigma_3\Gamma_3 \cos x) + C\sigma_4 \Gamma_4, $$ where $\Gamma_i$ are white noises that satisfy $\langle \Gamma_i(t)\rangle=0$ and $\langle \Gamma_i(t)\Gamma_j(t')\rangle=2\delta_{ij}\delta(t-t')$, is it possible to write out a Fokker-Planck equation of $P(x,t)$ for the given stochastic differential equation?
If it is generally not possible, what about for the case of $\sigma_1=0$?