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2015 Application of an averaging principle on foliated diffusions: topology of the leaves
Paulo Ruffino
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Electron. Commun. Probab. 20: 1-5 (2015). DOI: 10.1214/ECP.v20-3715


We consider an $\epsilon K$ transversal perturbing vector field in a foliated Brownian motion defined in a foliated tubular neighbourhood of an embedded compact submanifold in $\mathbb{R}^3$. We study the effective behaviour of the system under this $\epsilon$ perturbation. If the perturbing vector field $K$ is proportional to the Gaussian curvature at the corresponding leaf, we have that the transversal component, after rescaling the time by $t/\epsilon$, approaches a linear increasing behaviour proportional to the Euler characteristic of $M$, as $\epsilon$ goes to zero. An estimate of the rate of convergence is presented.


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Paulo Ruffino. "Application of an averaging principle on foliated diffusions: topology of the leaves." Electron. Commun. Probab. 20 1 - 5, 2015.


Accepted: 20 March 2015; Published: 2015
First available in Project Euclid: 7 June 2016

zbMATH: 1327.60159
MathSciNet: MR3327867
Digital Object Identifier: 10.1214/ECP.v20-3715

Primary: 60H10
Secondary: 58J37 , 58J65

Keywords: averaging principle , Brownian motion on manifolds , foliated stochastic flow


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