On symmetries of stochastic differential equations

摘要

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