Quasi Invariant Stochastic Flows of SDEs with Non-smooth Drifts on Riemannian Manifolds$^*$

Details Quasi Invariant Stochastic Flows of SDEs with Non-smooth Drifts on Riemannian Manifolds$^*$ Quasi Invariant Stochastic Flows of SDEs with Non-smooth Drifts on Riemannian Manifolds$^*$

2010-07-08

arxiv.org/abs/1007.1486v1

Mathematics

Probability

14 pages

Scientific paper

In this article we prove that stochastic differential equation (SDE) with
Sobolev drift on 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 Riemannian manifold.

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