On ADF Goodness-of-Fit Tests for Perturbed Dynamical Systems

We consider the problem of the construction of the goodness-of-fit tests for diffusion processes with small noise. The basic hypothesis is composite parametric and our goal is to obtain asymptotically distribution free tests. We propose two solutions. The first one is based on the change of time and the second test we obtain with the help of some linear transformation of the "natural" statistics.