Asymptotic equivalence for a null recurrent diffusion

Abstract

We establish that the model generated by the observation of the path of a one-dimensional null recurrent diffusion, when the parameter is the compactly supported drift, is asymptotically equivalent to a mixed Gaussian white noise experiment as the observation time T → ∞. The approximation is given in the sense of Le Cam's deficiency ͉-distance over Sobolev balls of smoothness order β > ½.