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Strong approximation of semimartingales and statistical processes
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  • Published: December 1996

Strong approximation of semimartingales and statistical processes

  • E. Eberlein1 &
  • M. Römersperger1 nAff2 

Probability Theory and Related Fields volume 104, pages 539–567 (1996)Cite this article

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  • 3 Citations

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Summary

As an application of general convergence results for semimartingales, exposed in their book ‘Limit Theorems for Stochastic Processes’, Jacod and Shiryaev obtained a fundamental result on the convergence of likelihood ratio processes to a Gaussian limit. We strengthen this result in a quantitative sense and show that versions of the likelihood ratio processes can be defined on the space of the limiting experiment such that we get pathwise almost sure approximations with respect to the uniform metric. The approximations are considered under both sequences of measures, the hypothesisP n and the alternative\(\overline {P^n } \). A consequence is e.g. an estimate for the speed of convergence in the Prohorov metric. New approximation techniques for stochastic processes are developed.

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Author information

Author notes
  1. M. Römersperger

    Present address: , Stadtstrasse 46, D-79104, Freiburg, Germany

Authors and Affiliations

  1. Institut für Mathematische Stochastik, Universität Freiburg, Hebelstrasse 27, D-79104, Freiburg, Germany

    E. Eberlein & M. Römersperger

Authors
  1. E. Eberlein
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  2. M. Römersperger
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This article was processed by the author using the LATEX style filepljourIm from Springer-Verlag.

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Eberlein, E., Römersperger, M. Strong approximation of semimartingales and statistical processes. Probab. Th. Rel. Fields 104, 539–567 (1996). https://doi.org/10.1007/BF01198166

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  • Received: 21 June 1994

  • Accepted: 27 November 1995

  • Issue Date: December 1996

  • DOI: https://doi.org/10.1007/BF01198166

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Mathematics Subject Classification (1991)

  • 62E20
  • 60F17
  • 60G07
  • 60G15
  • 60G17
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