  We study the differential forms over the frame bundle of the based loop
space. They are stochastics in the sense that we put over this frame bundle a
probability measure. In order to understand the curvatures phenomena which
appear when we look at the Lie bracket of two horizontal vector fields, we
impose some regularity assumptions over the kernels of the differential forms.
This allows us to define an exterior stochastic differential derivative over
these forms.
