| Full text | |
| Author(s): |
Total Authors: 2
|
| Affiliation: | [1] Univ Estadual Campinas, Campinas, SP - Brazil
[2] Univ Estadual Paulista UNESP, Bauru, SP - Brazil
Total Affiliations: 2
|
| Document type: | Journal article |
| Source: | DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL; v. 35, n. 4, p. 625-654, OCT 1 2020. |
| Web of Science Citations: | 0 |
| Abstract | |
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. (AU) | |
| FAPESP's process: | 15/07278-0 - Stochastic dynamics: analytical and geometrical aspects with applications |
| Grantee: | Paulo Regis Caron Ruffino |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 18/16568-0 - An averaging principle for stochastic differential equations |
| Grantee: | Fabiano Borges da Silva |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 12/18780-0 - Geometry of control systems, dynamical and stochastics systems |
| Grantee: | Marco Antônio Teixeira |
| Support Opportunities: | Research Projects - Thematic Grants |