Abstract1 Inspired by the fundamental work of T.J. Lyons (loc.cit), we develop a theory of curvilinear integrals along a new kind of enriched paths in IR d . We apply these methods to the fractional Brownian Motion, and prove a support theorem for SDE driven by the Skorohod fBM of Hurst parameter H > 1/4.

Abstl~et. We construct a 'Hausdorff measure' of finite co-dimension on the Wiener space. We then extend the Federer co-area Formula to this Wiener space for functions with the sole condition that they belong to the first Sobolev space. An explicit formula for the density of the images of the Wiener measure under such functions follows naturally from this. As a corollary, this yields a new and easy proof of the Kr6e-Watanabe theorem concerning the regularity of the images of the Wiener measure.Mathematies Subject Cl~aifieations (1991). 28A50, 28C20, 46E35, 46F05, 46F25, 46G12, 60(315, 60H07.

A non-commutative version of the sewing lemma [1] is proved, with some applications.1 Definition : We say that a function V (t) defined on [0, T [ is a control function if it is non decreasing, V (0) = 0 and n≥1 V (1/n) < ∞.As easily seen, this is equivalent to the propertyfor every t ≥ 0. For example, t α and t/(log t −1 ) α with α > 1 are control functions.Observe that we havea control function. Then there exists a unique function ϕ(t) on [0, T [, up to an additive constant, such that |ϕ(b) − ϕ(a) − µ(a, b)| ≤ V (b − a) Proof : Put µ ′ (a, b) = µ(a, c) + µ(c, b) for c = (a + b)/2, and µ (n+1) = µ (n)′ . We easily get for n ≥ 0 a) converges, and the sequence µ (n) (a, b) converges to a limit u(a, b). For c = (a + b)/2 we haveWe say that u is midpoint-additive. Now, we prove that u is the unique midpoint-additive function with the inequalityand by induction |v(a, b) − u(a, b)| ≤ 2 n K.V [2 −n (b − a)] which vanishes as n → ∞ as mentioned above. Let k be an integer k ≥ 3, and take the function

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