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Local asymptotic normality and mixed normality for Markov statistical models
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  • Published: March 1990

Local asymptotic normality and mixed normality for Markov statistical models

  • Reinhard Höpfner1,
  • Jean Jacod2 &
  • Lucia Ladelli2 

Probability Theory and Related Fields volume 86, pages 105–129 (1990)Cite this article

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Summary

We prove local asymptotic normality (resp. local asymptotic mixed normality) of a statistical experiment, when the observation is a positive-recurrent (resp. null-recurrent, with an additional technical assumption) Markov chain or Markov step process, under rather mild regularity assumptions on the transition kernel for Markov chains, on the infinitesimal generator for Markov processes. The proof makes intensive use of Hellinger processes, thus avoiding almost completely to study the more complicated structure of the likelihoods themselves.

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Author information

Authors and Affiliations

  1. Institut für Mathematische Stochastik, Albert-Ludwigs-Universität, Hebelstrasse 27, D-7800, Freiburg i.Br., Federal Republic of Germany

    Reinhard Höpfner

  2. Laboratoire de Probabilités, Université Pierre et Marie Curie (Paris-6), Tour 56 (3o étage), 4 Place Jussieu, F-75252, Paris Cedex 05, France

    Jean Jacod & Lucia Ladelli

Authors
  1. Reinhard Höpfner
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  2. Jean Jacod
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  3. Lucia Ladelli
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Höpfner, R., Jacod, J. & Ladelli, L. Local asymptotic normality and mixed normality for Markov statistical models. Probab. Th. Rel. Fields 86, 105–129 (1990). https://doi.org/10.1007/BF01207516

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  • Received: 06 April 1989

  • Revised: 21 February 1990

  • Issue Date: March 1990

  • DOI: https://doi.org/10.1007/BF01207516

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Keywords

  • Statistical Model
  • Markov Chain
  • Stochastic Process
  • Probability Theory
  • Statistical Experiment
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