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Quasi-invariant stochastic flows of SDEs with non-smooth drifts on compact manifolds
- Source :
- Stochastic Processes and their Applications. 121(6):1373-1388
- Publication Year :
- 2011
- Publisher :
- Elsevier BV, 2011.
-
Abstract
- In this article we prove that stochastic differential equation (SDE) with Sobolev drift on a compact Riemannian manifold admits a unique ν -almost everywhere stochastic invertible flow, where ν is the Riemannian measure, which is quasi-invariant with respect to ν . In particular, we extend the well-known DiPerna-Lions flows of ODEs to SDEs on a Riemannian manifold.
- Subjects :
- Statistics and Probability
DiPerna-Lions flow
Riemannian manifold
Applied Mathematics
Mathematical analysis
Mathematics::Analysis of PDEs
Manifold
Sobolev space
Stochastic differential equation
Flow (mathematics)
Stochastic flow
Hardy-Littlewood maximal function
Modeling and Simulation
Modelling and Simulation
Almost everywhere
Invariant measure
Mathematics::Differential Geometry
Invariant (mathematics)
Sobolev drift
Mathematics
Subjects
Details
- ISSN :
- 03044149
- Volume :
- 121
- Issue :
- 6
- Database :
- OpenAIRE
- Journal :
- Stochastic Processes and their Applications
- Accession number :
- edsair.doi.dedup.....5298097e8d7d2aaa064a324243d4236c
- Full Text :
- https://doi.org/10.1016/j.spa.2011.03.001