Autor(es)

Melo, Alison M. ; Morgado, Leandro B. ; Ruffino, Paulo R.

• Tipo de documento: Artigo Científico
• Fonte: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B; v. 21, n. 9, p. 10-pg., 2016-11-01.

Resumo

Consider a manifold M endowed locally with a pair of complementary distributions Delta(H) (R) Delta(V) = TM and let Diff(Delta(H), M) and Diff(Delta(V), M) be the corresponding Lie subgroups generated by vector fields in the corresponding distributions. We decompose a stochastic flow with jumps, up to a stopping time, as phi(t) = xi(t) o psi(t), where xi(t) is an element of Diff(Delta(H), M) and psi(t) is an element of Diff(Delta(V), M). Our main result provides Stratonovich stochastic differential equations with jumps for each of these two components in the corresponding infinite dimensional Lie groups. We present an extension of the It (o) over cap -Ventzel-Kunita formula for stochastic flows with jumps generated by classical Marcus equation (as in Kurtz, Pardoux and Protter [11]). The results here correspond to an extension of Catuogno, da Silva and Ruffino [4], where this decomposition was studied for the continuous case. (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: 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 - Dynamical phenomena in complex networks: fundamentals and applications
• Beneficiário: Elbert Einstein Nehrer Macau
• Modalidade de apoio: Auxílio à Pesquisa - Temático