Asymptotic symmetry and asymptotic solutions to Ito stochastic differential equations

Abstract

We consider several aspects of conjugating symmetry methods, including the method of invariants, with an asymptotic approach. In particular we consider how to extend to the stochastic setting several ideas which are well established in the deterministic one, such as conditional, partial and asymptotic symmetries. A number of explicit examples are presented.

Keywords

• symmetry
• stochastic differential equations
• asymptotic properties
• conserved quantities
• invariance