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Pré-Publication, Document De Travail Année : 2014

Additive functionals and push forward measures under Veretennikov's flow

Résumé

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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Dates et versions

hal-00949736 , version 1 (20-02-2014)

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  • HAL Id : hal-00949736 , version 1

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