Zusammenfassung für den Vortrag am 24.04.2013 (16:15 Uhr)Seminar DYNAMISCHE SYSTEME
Paulo R. C. Ruffino (Universidade Estadual de Campinas, Brazil, and Humboldt-Universität zu Berlin, Germany)
An averaging principle for diffusions in foliated manifolds
Consider a stochastic differential equation on a foliated manifold whose trajectories lay on compact leaves. We investigate the effective behaviour of a small transversal perturbation of order ϵ. 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 ϵ 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.