# Additive functionals and push forward measures under Veretennikov's flow

Abstract : In this work, we will be interested in the push forward measure $(\vf_t)_*\gamma$, where $\vf_t$ is defined by the stochastic differential equation \begin{equation*} d\vf_t(x)=dW_t + \ba(\vf_t(x))dt, \quad \vf_0(x)=x\in\mbR^m, \end{equation*} and $\gamma$ is the standard Gaussian measure. We will prove the existence of density under the hypothesis that the divergence $\div(\ba)$ is not a function, but a signed measure belonging to a Kato class; the density will be expressed with help of the additive functional associated to $\div(\ba)$.
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https://hal.archives-ouvertes.fr/hal-00949736
Contributor : Shizan Fang <>
Submitted on : Thursday, February 20, 2014 - 10:44:06 AM
Last modification on : Friday, June 8, 2018 - 2:50:07 PM
Long-term archiving on : Tuesday, May 20, 2014 - 2:48:20 PM

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Fang_PilipenkoSW.pdf
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• HAL Id : hal-00949736, version 1

### Citation

Shizan Fang, Andrey Pilipenko. Additive functionals and push forward measures under Veretennikov's flow. 2014. ⟨hal-00949736⟩

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