Search for the symmetry of the Fokker-Planck equation (Q1083099)

It is shown that the Fokker-Planck equations with linear drift \(\gamma\) x and nonlinear drift \(\gamma x+\delta /x\), i.e. the Rayleigh process, have exact symmetries on their own solution manifolds, the sl(2,R)\(\otimes\) Weyl algebra and the sl(2,R)\(\otimes I\), respectively. The symmetries of these two types of processes for \(1+2\)-dimensional cases are explicitly found out too.