Quasi-invariant stochastic flows of SDEs with non-smooth drifts on compact manifolds

In this article we prove that stochastic differential equation (SDE) with Sobolev drift on a compact Riemannian manifold admits a unique [nu]-almost everywhere stochastic invertible flow, where [nu] is the Riemannian measure, which is quasi-invariant with respect to [nu]. In particular, we extend the well-known DiPerna-Lions flows of ODEs to SDEs on a Riemannian manifold.

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Year of publication:	2011
Authors:	Zhang, Xicheng
Published in:	Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 121.2011, 6, p. 1373-1388
Publisher:	Elsevier
Keywords:	Stochastic flow DiPerna-Lions flow Hardy-Littlewood maximal function Riemannian manifold Sobolev drift

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10009023942