Derivation of Lie Groups for Some Higher Order Stochastic Differential Equations

In this paper, we give examples of the construction of Lie groups forsome examples of second and third order stochastic differential equations of physicalinterest. Determining equations are derived for admitted Lie groups of transformationsthat transform Brownian motion terms into Brownian motion terms. The examples include both fiber-preserving and non-fiber-preserving transformations. It is proved by direct transformation that the derived Lie groups transformthe original stochastic equations into stochastic equations with the same solutions.