An averaging principle for diffusions in foliated spaces

• Gonzales-Gargate, Ivan I. ^[1] ; Ruffino, Paulo R. ^[1]
  1. [1] Universidade Estadual de Campinas

     Universidade Estadual de Campinas

     Brasil

     
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 44, Nº. 1, 2016, págs. 567-588
• Idioma: inglés
• DOI: 10.1214/14-AOP982
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• Resumen

  • 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 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.