“…The development of a Lie symmetry analysis for stochastic differential equations (SDEs) and general random systems is relatively recent (see, e.g., [1,2,17,18,19,20,26,25,27,33,38] for some recent developments in the non-variational case). For stochastic systems arising from a variational framework, it is certainly interesting to study the relation between their symmetries and functionals which are conserved by their flow, and, in particular, to establish stochastic generalizations of Noether theorem.…”