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Application of an averaging principle on foliated diffusions: topology of the leaves (1408.1154v1)
Published 6 Aug 2014 in math.PR
Abstract: 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 $\R3$. 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.