Azéma, J. (ed.) et al., Séminaire de probabilités XXX. Berlin: Springer. Lect. Notes Math. 1626, 68-99 (1996).
Let be a compact, finite-dimensional, Riemannian manifold, the space of paths and the space of free loops on .
The article consists of two parts. The first part, using a regularity defined by D. Nualart and E. Pardoux [Probab. Theory Relat. Fields 78, No. 4, 535-581 (1988; Zbl 0629.60061)], is building a version of stochastic exterior derivative on the space of -forms in Nualart-Pardoux sense. This stochastic exterior derivative leads to , the entire Nualart-Pardoux cohomology, , the Bismut-Nualart-Pardoux cohomology of order , and (flat). It is proved that .
In the second part, following E. Getzler, J. Jones and S. Petrack [Topology 30, No. 3, 339-371 (1991; Zbl 0729.58004)] a commutative diagram of complexes is used to prove the equality between the entire Hochschild cohomology and the stochastic cohomology on the loop space.