AN AVERAGING PRINCIPLE FOR DIFFUSIONS IN FOLIATED SPACES

Author(s)

Gonzales-Gargate, Ivan I. ^[1] ; Ruffino, Paulo R. ^[1]

Affiliation

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

• Document type: Journal article
• Source: ANNALS OF PROBABILITY; v. 44, n. 1, p. 567-588, JAN 2016.
• Web of Science Citations: 6

Abstract

Consider an SDE on a foliated manifold whose trajectories lay on compact leaves. We investigate the effective behavior of a small transversal perturbation of order epsilon. An average principle is shown to hold such that the component transversal to the leaves converges to the solution of a deterministic ODE, according to the average of the perturbing vector field with respect to invariant measures on the leaves, as a goes to zero. An estimate of the rate of convergence is given. These results generalize the geometrical scope of previous approaches, including completely integrable stochastic Hamiltonian system. (AU)

• FAPESP's process: 12/03992-1 - Dynamics and geometry of stochastic flows
• Grantee: Paulo Regis Caron Ruffino
• Support Opportunities: Scholarships abroad - Research
• 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