Symmetries of first-order stochastic ordinary differential equations revisited

Symmetries of stochastic ordinary differential equations (SODEs) are analysed. This work focuses on maintaining the properties of the Weiner processes after the application of infinitesimal transformations. The determining equations (DEs) for first-order SODEs are derived in an Ito calculus context. These DEs are non-stochastic. This article reconciles earlier works in this area.