Degenerate Semigroups and Stochastic Flows of Mappings in Foliated Manifolds

Autor(es)

da Costa, Paulo Henrique P. ^[1] ; Ruffino, Paulo R. ^[1]

Afiliação do(s) autor(es)

^[1] Univ Estadual Campinas, Dept Matemat, BR-13083859 Campinas, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: POTENTIAL ANALYSIS; v. 43, n. 3, p. 461-480, OCT 2015.
• Citações Web of Science: 0

Resumo

Let be a foliated compact Riemannian manifold. We consider a family of compatible Feller semigroups in C(M (n) ) associated to laws of the n-point motion. Under some assumptions (Le Jan and Raimond, Ann. Probab. 32:1247-1315, 2004) there exists a stochastic flow of measurable mappings in M. We study the degeneracy of these semigroups such that the flow of mappings is foliated, i.e. each trajectory lays in a single leaf of the foliation a.s, hence creating a geometrical obstruction for coalescence of trajectories in different leaves. As an application, an averaging principle is proved for a first order perturbation transversal to the leaves. Estimates for the rate of convergence are calculated. (AU)

• Processo FAPESP: 11/50151-0 - Fenômenos dinâmicos em redes complexas: fundamentos e aplicações
• Beneficiário: Elbert Einstein Nehrer Macau
• Linha de fomento: Auxílio à Pesquisa - Temático
• Processo FAPESP: 12/03992-1 - Dinâmica e geometria de fluxos estocásticos
• Beneficiário: Paulo Regis Caron Ruffino
• Linha de fomento: Bolsas no Exterior - Pesquisa