On symmetries of the Fokker–Planck equation

This paper is devoted to Lie point symmetries of the Fokker–Planck (FP) equation. It describes the relation between symmetries and first integrals of stochastic differential equations (SDEs) and symmetries of the associated FP equations. This relation is illustrated on symmetries of (1 + 1)-dimensional FP equations specified by Lie group classification of the scalar SDE. Further, it is used to find symmetries of (1 + 2)-dimensional FP equations specified by Lie group classification of the system of two SDEs.