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Asymptotic statistical equivalence for scalar ergodic diffusions
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  • Published: 03 May 2005

Asymptotic statistical equivalence for scalar ergodic diffusions

  • Arnak Dalalyan1 &
  • Markus Reiß2 

Probability Theory and Related Fields volume 134, pages 248–282 (2006)Cite this article

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  • 20 Citations

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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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Author information

Authors and Affiliations

  1. Laboratoire de Probabilités, Université Paris VI, Place Jussieu, 75252, Paris Cedex 05, France

    Arnak Dalalyan

  2. Weierstraß Institute for Applied Analysis and Stochastics, Mohrenstraße 39, 10117, Berlin, Germany

    Markus Reiß

Authors
  1. Arnak Dalalyan
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  2. Markus Reiß
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Corresponding author

Correspondence to Arnak Dalalyan.

Additional information

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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Cite this article

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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  • Received: 18 March 2004

  • Revised: 21 November 2004

  • Published: 03 May 2005

  • Issue Date: February 2006

  • DOI: https://doi.org/10.1007/s00440-004-0416-1

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Mathematics Subject Classification (2000)

  • 62B15
  • 62C05
  • 62G20
  • 62M99

Key words or phrases

  • Asymptotic equivalence
  • Statistical experiment
  • Le Cam distance
  • Ergodic diffusion
  • Local time
  • Mixed Gaussian white noise
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