On symmetries of stochastic differential equations

This note can be considered as a supplement to article [8]. Its purpose is twofold. First, to show that symmetries of Itô stochastic differential equations form a Lie algebra. Second, to provide more precise formulation of the relation between symmetries of SDEs and symmetries of the associated Fokker–Planck equation. Relation between first integrals of SDEs and symmetries of the associated Fokker–Planck equation is also considered.

► It is proved that symmetries of Itô SDEs form a Lie algebra.
► Relation between symmetries of SDEs and symmetries of FP equations is provided.
► Relation between first integrals of SDEs and symmetries of FP equations is provided.