Transport equations and quasi-invariant flows on the Wiener space

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Abstract

We shall investigate on vector fields of low regularity on the Wiener space, with divergence having low exponential integrability. We prove that the vector field generates a flow of quasi-invariant measurable maps with density belonging to the space LlogL. An explicit expression for the density is also given.

MSC

60H07
65L05
76M35

Keywords

Wiener space
Transport equations
Commutator estimate
Quasi-invariant flows
Malliavin calculus

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