Open Access
January 2016 An averaging principle for diffusions in foliated spaces
Ivan I. Gonzales-Gargate, Paulo R. Ruffino
Ann. Probab. 44(1): 567-588 (January 2016). DOI: 10.1214/14-AOP982


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 $\varepsilon$. 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 $\varepsilon$ 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.


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Ivan I. Gonzales-Gargate. Paulo R. Ruffino. "An averaging principle for diffusions in foliated spaces." Ann. Probab. 44 (1) 567 - 588, January 2016.


Received: 1 January 2013; Revised: 1 March 2014; Published: January 2016
First available in Project Euclid: 2 February 2016

zbMATH: 06571511
MathSciNet: MR3456346
Digital Object Identifier: 10.1214/14-AOP982

Primary: 58J37 , 58J65 , 60H10

Keywords: averaging principle , foliated diffusion , rescaled stochastic systems , Stochastic flows

Rights: Copyright © 2016 Institute of Mathematical Statistics

Vol.44 • No. 1 • January 2016
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