Degenerate Semigroups and Stochastic Flows of Mappings in Foliated Manifolds

Author(s)

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

Affiliation

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

• Document type: Journal article
• Source: POTENTIAL ANALYSIS; v. 43, n. 3, p. 461-480, OCT 2015.
• Web of Science Citations: 0

Abstract

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)

• FAPESP's process: 11/50151-0 - Dynamical phenomena in complex networks: fundamentals and applications
• Grantee: Elbert Einstein Nehrer Macau
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 12/03992-1 - Dynamics and geometry of stochastic flows
• Grantee: Paulo Regis Caron Ruffino
• Support Opportunities: Scholarships abroad - Research