A STOCHASTIC INVARIANTIZATION METHOD FOR ITÔ STOCHASTIC PERTURBATIONS OF DIFFERENTIAL EQUATIONS

In general, adding a stochastic perturbation to a dierential equation possessing an invariant manifold destroys the invariance as far as the Ito formalism is used. In this article, we propose an invariantization method for perturbations in the Ito case which can be used to restore invariance. We then apply our results to develop a stochastic version of the Landau-Lifshitz equation. We discuss in particular previous results obtained by Etore and al. in [6].