  This paper investigates the problem to determine whether a given stochastic
process generates a sampled Brownian filtration. A fairly general sufficient
condition is obtained by applying the Frank H. Clarke contraction criteria to a
functional whose construction relies on the quasi-invariance properties of a
sampled Wiener measure. The latter are investigated from the precise analytic
structure underlying this sampled Brownian motion. In particular, the
Cameron-Martin space is identified from usual Lebesgue integrals over a
Guseinov measure. As an application we obtain sufficient conditions for the
existence of a solution to a class of not necessarily Markovian stochastic
differential equations driven by a sampled Brownian motion. By taking a
sampling times set which coincides with the unit interval, the results apply to
continuous time models.
