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

Xicheng Zhang

Stochastic Processes and their Applications, 2011, vol. 121, issue 6, 1373-1388

Abstract: 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.

Keywords: Stochastic; flow; DiPerna-Lions; flow; Hardy-Littlewood; maximal; function; Riemannian; manifold; Sobolev; drift (search for similar items in EconPapers)
Date: 2011
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