6533b820fe1ef96bd1279a15

RESEARCH PRODUCT

Additive functionals and push forward measures under Veretennikov's flow

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16 pages; 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 $\div(\ba)$.