Lie symmetry reductions and integrability of approximated small delay stochastic differential equations

Abstract

This paper presents Lie symmetries of small delay stochastic differential equations (SDSDE). We derive an approximation of a small delay stochastic differential equation (SDSDE) equivalence to a non-delay stochastic differential equation, with an intent of constructing the corresponding Lie symmetry algebras. The method is applied to different examples of small delay stochastic differential equations to obtain symmetry algebras, reductions and solutions of the approximated non-delay stochastic differential equation.