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Asymptotic local equivalence in the sense of Le Cam is established forinference on the drift in multidimensional ergodic diffusions and anaccompanying sequence of Gaussian shift experiments. The nonparametric localneighbourhoods can be attained for any dimension, provided the regularity ofthe drift is sufficiently large. In addition, a heteroskedastic Gaussianregression experiment is given, which is also locally asymptotically equivalentand which does not depend on the centre of localisation. For one direction ofthe equivalence an explicit Markov kernel is constructed.Comment: 03 May 2005, 23 page

Asymptotic statistical equivalence for ergodic diffusions: the multidimensional case