I have a bidimensional Fokker-Planck equation to solve, namely,
$$ \frac{\partial p}{\partial t} = \frac{\sigma_{1}^{2}}{2} \frac{\partial^{2} p}{\partial I^{2}} - \frac{\partial }{\partial S} (b_{1}(S,I) p) - \frac{\partial }{\partial I}(b_{2} (S,I) p) \,\, , $$
where,
$$ b_{1} = -aSI \,\, , \\ b_{2} = aSI-\mu I + cI -cSI-cI^2 \,\, . $$
My initial and Neumann conditions are the following,
$$ p(S,I,0) = \delta (S-S_{0},I-I_{0}) \,\, , \\ \lim_{S,I \to \pm \infty} p(S,I,t)= \lim_{S,I \to \pm \infty} \partial_{S} p(S,I,t) = \partial_{I} p(S,I,t) = 0 \,\, . $$
How can I solve this FP equation? Can I apply separation of variables?