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

Xicheng Zhang

doi:10.1016/j.spa.2011.03.001

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

Xicheng Zhang^*

^*Corresponding author for this work

Wuhan University

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

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.

Original language	English
Pages (from-to)	1373-1388
Number of pages	16
Journal	Stochastic Processes and their Applications
Volume	121
Issue number	6
DOIs	https://doi.org/10.1016/j.spa.2011.03.001
Publication status	Published - Jun 2011
Externally published	Yes

Keywords

DiPerna-Lions flow
Hardy-Littlewood maximal function
Riemannian manifold
Sobolev drift
Stochastic flow

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10.1016/j.spa.2011.03.001

Cite this

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title = "Quasi-invariant stochastic flows of SDEs with non-smooth drifts on compact manifolds",

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.",

keywords = "DiPerna-Lions flow, Hardy-Littlewood maximal function, Riemannian manifold, Sobolev drift, Stochastic flow",

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AB - 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.

KW - DiPerna-Lions flow

KW - Hardy-Littlewood maximal function

KW - Riemannian manifold

KW - Sobolev drift

KW - Stochastic flow

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VL - 121

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JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 6

ER -

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

Abstract

Keywords

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