Ermakov-Ray-Reid systems with additive noise

Abstract

"Using the methods developed by us in Cervantes-López et al. (2014) for multiplicative noises, we present results on the effects of the additive noise on the Ermakov-Lewis invariant. This case can be implemented in the Euler-Maruyama numerical method if the additive noise is considered as the forcing term of the parametric oscillator and presented as a particular case of the Ermakov-Ray-Reid systems. The results are obtained for the same particular examples as for the multiplicative noise and show a tendency to less robustness of the Ermakov-Lewis invariant to the additive noise as compared to the multiplicative noise."