Extension of time for decomposition of stochastic flows in spaces with complementary foliations

Autor(es)

Morgado, Leandro ^[1] ; Ruffino, Paulo R. ^[1]

Afiliação do(s) autor(es)

^[1] Univ Estadual Campinas, Dept Matemat, BR-13081970 Campinas, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Electronic Communications in Probability; v. 20, p. 1-9, MAY 17 2015.
• Citações Web of Science: 1

Resumo

Let M be a manifold equipped (locally) with a pair of complementary foliations. In Catuogno, da Silva and Ruffino {[}4], it is shown that, up to a stopping time tau, a stochastic flow of local diffeomorphisms phi(t) in M can be decomposed in diffeomorphisms that preserves this foliations. In this article we present techniques which allow us to extend the time of this decomposition. For this extension, we use two techniques: In the first one, assuming that the vector fields of the system commute with each other, we apply Marcus equation to jump nondecomposable diffeomorphisms. The second approach deals with the general case: we introduce a `stop and go' technique that allows us to construct a process that follows the original flow in the `good zones' for the decomposition, and remains paused in `bad zones'. Among other applications, our results open the possibility of studying the asymptotic behaviour of each component. (AU)

• 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
• Processo FAPESP: 11/14797-2 - Dinâmica estocástica em espaços folheados
• Beneficiário: Leandro Batista Morgado
• Modalidade de apoio: Bolsas no Brasil - Doutorado Direto
• Processo FAPESP: 11/50151-0 - Fenômenos dinâmicos em redes complexas: fundamentos e aplicações
• Beneficiário: Elbert Einstein Nehrer Macau
• Modalidade de apoio: Auxílio à Pesquisa - Temático