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Intégration géométrique sur l’espace de Wiener. (Geometric integration on the Wiener space). (French) Zbl 0656.60046
For a suitably smooth Wiener functional $$\Phi$$ it is shown that the set $$V_{\xi}=\{w: \Phi (w)=\xi \}$$ can be viewed as a submanifold in Wiener space, of which the finite codimension is the dimension of the range of $$\Phi$$. The set $$V_{\xi}$$ is defined only modulo slim sets, since the same is true for $$\Phi$$. The set $$V_{\xi}$$ arises as the support of the measure obtained by conditioning on $$\Phi =\xi$$, and the measure can be obtained using Watanabe’s distributional version of Malliavin calculus. A co-area formula and a Stokes formula are obtained.
Reviewer: W.S.Kendall

##### MSC:
 60G07 General theory of stochastic processes 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis) 58J65 Diffusion processes and stochastic analysis on manifolds