Abstract
For scalar diffusion models with unknown drift function asymptotic equivalence in the sense of Le Cam's deficiency between statistical experiments is considered under long-time asymptotics. A local asymptotic equivalence result is established with an accompanying sequence of simple Gaussian shift experiments. Corresponding globally asymptotically equivalent experiments are obtained as compound experiments. The results are extended in several directions including time discretisation. An explicit transformation of decision functions from the Gaussian to the diffusion experiment is constructed.
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The authors acknowledge the financial support provided through the European Community's Human Potential Programme under contract HPRN-CT-2000-00100, DYNSTOCH
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Dalalyan, A., Reiß, M. Asymptotic statistical equivalence for scalar ergodic diffusions. Probab. Theory Relat. Fields 134, 248–282 (2006). https://doi.org/10.1007/s00440-004-0416-1
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DOI: https://doi.org/10.1007/s00440-004-0416-1