Decomposition of stochastic flow and an averaging principle for slow perturbations

Autor(es)

Ledesma, Diego Sebastian ^[1] ; Borges da Silva, Fabiano ^[2]

Afiliação do(s) autor(es)

^[1] Univ Estadual Campinas, Campinas, SP - Brazil

^[2] Univ Estadual Paulista UNESP, Bauru, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL; v. 35, n. 4, p. 625-654, OCT 1 2020.
• Citações Web of Science: 0

Resumo

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)

• Processo FAPESP: 15/07278-0 - Dinâmica estocástica: aspectos analíticos, geométricos e aplicações
• Beneficiário: Paulo Regis Caron Ruffino
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 18/16568-0 - Um princípio de médias para equações diferenciais estocásticas
• Beneficiário: Fabiano Borges da Silva
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 12/18780-0 - Geometria de sistemas de controle, sistemas dinâmicos e estocásticos
• Beneficiário: Marco Antônio Teixeira
• Modalidade de apoio: Auxílio à Pesquisa - Temático