A stochastic invariantization method for It\^o stochastic perturbations of differential equations
Mathematical Physics
2018-09-26 v1 Dynamical Systems
math.MP
Abstract
In general, adding a stochastic perturbation to a differential equation possessing an invariant manifold destroys the invariance as far as the It\^o formalism is used. In this article, we propose an invariantization method for perturbations in the It\^o 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 [P. \'Etor\'e, S.Labb\'e , J. Lelong, Long time behaviour of a stochastic nanoparticle, J. Differential Equations 257 (2014), 2115-2135].
Keywords
Cite
@article{arxiv.1809.09363,
title = {A stochastic invariantization method for It\^o stochastic perturbations of differential equations},
author = {Jacky Cresson and Yasmina Kheloufi and Khadra Nachi},
journal= {arXiv preprint arXiv:1809.09363},
year = {2018}
}
Comments
15 pages