Artículos de revistas
Decomposition of stochastic flow and an averaging principle for slow perturbations
Fecha
2020-01-01Registro en:
Dynamical Systems.
1468-9375
1468-9367
10.1080/14689367.2020.1769031
2-s2.0-85086665466
Autor
Universidade Estadual de Campinas (UNICAMP)
Universidade Estadual Paulista (Unesp)
Institución
Resumen
In this work we use the stochastic flow decomposition technique to get components that represent the dynamics of the slow and fast motion of a stochastic differential equation with a random perturbation. Assuming a Lipschitz condition for vector fields and an average principle we get an approximation for the slow motion. To obtain the estimate for the rate of convergence we use a distance function which is defined in terms of the height functions associated to an isometric embedding of the manifold into the Euclidean space. This metric is topologically equivalent to the Riemannian distance given by the infimum of the lengths of all admissible curves between two points and works well with stochastic calculation tools. Finally, we get an estimate for the approximation between the solution of perturbed system and the original process provided by the unperturbed.