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Large deviations w.r.t. quasi-every starting point for symmetric right processes on general state spaces
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  • Published: December 1994

Large deviations w.r.t. quasi-every starting point for symmetric right processes on general state spaces

  • Stefan Mück1 

Probability Theory and Related Fields volume 99, pages 527–548 (1994)Cite this article

Summary

In the work of Donsker and Varadhan, Fukushima and Takeda and that of Deuschel and Stroock it has been shown, that the lower bound for the large deviations of the empirical distribution of an ergodic symmetric Markov process is given in terms of its Dirichlet form. We give a short proof generalizing this principle to general state spaces that include, in particular, infinite dimensional and non0metrizable examples. Our result holds w.r.t. quasi-every starting point of the Markov process. Moreover we show the corresponding weak upper bound w.r.t. quasi-every starting point.

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Authors and Affiliations

  1. Institut für Angewandte Mathematik Bonn, Wegelerstrasse 6, D-53115, Bonn, Germany

    Stefan Mück

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  1. Stefan Mück
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Additional information

This research was supported by the Graduiertenkolleg “Algebraische, analytische und geometrische Methoden und ihre Wechselwirkung in der modernen Mathematik”, Bonn

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Cite this article

Mück, S. Large deviations w.r.t. quasi-every starting point for symmetric right processes on general state spaces. Probab. Th. Rel. Fields 99, 527–548 (1994). https://doi.org/10.1007/BF01206231

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  • Received: 23 July 1993

  • Revised: 14 February 1994

  • Issue Date: December 1994

  • DOI: https://doi.org/10.1007/BF01206231

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Mathematics Subject Classification

  • 60F10
  • 31C25
  • 60J40
  • 60J45
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