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Diffusion approximation for nonparametric autoregression
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  • Published: December 1998

Diffusion approximation for nonparametric autoregression

  • Grigori Milstein1 &
  • Michael Nussbaum1 

Probability Theory and Related Fields volume 112, pages 535–543 (1998)Cite this article

  • 101 Accesses

  • 18 Citations

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Abstract.

A nonparametric statistical model of small diffusion type is compared with its discretization by a stochastic Euler difference scheme. It is shown that the discrete and continuous models are asymptotically equivalent in the sense of Le Cam's deficiency distance for statistical experiments, when the discretization step decreases with the noise intensity ε.

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  1. Weierstrass Institute, Mohrenstr. 39, D-10117 Berlin, Germany, , , , , , DE

    Grigori Milstein & Michael Nussbaum

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  1. Grigori Milstein
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  2. Michael Nussbaum
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Received: 12 April 1996 / Revised version: 29 October 1997

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Cite this article

Milstein, G., Nussbaum, M. Diffusion approximation for nonparametric autoregression. Probab Theory Relat Fields 112, 535–543 (1998). https://doi.org/10.1007/s004400050199

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  • Issue Date: December 1998

  • DOI: https://doi.org/10.1007/s004400050199

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  • Mathematics Subject Classification (1991): Primary 62M10; Secondary 62G07
  • 62B15
  • 60J60
  • 60H10.
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