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Divergence sur l’espace de Wiener et relèvement d’opérateurs différentiels. (French) Zbl 0548.46035

Summary: The following expression is given for the k-times iterated divergence of the product Fg of two functions F and g on the Wiener space \(\Omega\) : \[ (DIV^ k(F.g))(\omega)=\sum^{k}_{l=0}\left( \begin{matrix} k\\ l\end{matrix} \right)<DIV^{k-l}F(\omega),\quad D^ lg(\omega)>_ l. \] This formula permits an equivalent presentation of P. Malliavin’s lifting of vector fields on the Wiener space. This is illustrated by a result concerning the decay of probability densities.

MSC:

46F25 Distributions on infinite-dimensional spaces
28C20 Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.)
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