ABSTRACT
Lie point symmetries of Itô stochastic differential equations (SDEs) are considered. They correspond to Lie group transformations of the independent variable (time) and dependent variables, which preserve the differential form of the SDEs and properties of Brownian motion. In the considered framework transformations of Brownian motion are generated by random time change. There are provided some properties of the SDEs symmetries: the symmetries form a Lie algebra, there is a relation between symmetries and first integrals, and for some classes of SDEs there are results on maximal dimensionality of the admitted symmetry algebras. The symmetries can be used to construct Lie symmetry group classifications and to integrate SDEs with the help of quadratures. The relation to symmetries of the associated Fokker-Planck (FP) equation is also mentioned.
