Exponential mean-square stability properties of stochastic linear multistep methods

Abstract The aim of this paper is the analysis exponential mean-square stability properties nonlinear stochastic linear multistep methods. In particular it known that, under certain hypothesis on drift and diffusion terms equation, contractivity visible: qualitative feature exact problem here analysed numerical perspective, to understand whether a method can provide an analogous behaviour which restrictions employed stepsize should be imposed in order reproduce contractive behaviour. Numerical experiments confirming theoretical are also given.