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Large Deviations for Stationary Gaussian Processes

  • M. D. Donsker
  • S. R. S. Varadhan

Abstract

In their previous work on large deviations the authors always assumed the base process to be Markovian whereas here they consider the base process to be stationary Gaussian. Similar large deviation results are obtained under natural hypotheses on the spectral density function of the base process. A rather explicit formula for the entropy involved is also obtained.

Keywords

Probability Measure Spectral Measure Lower Semicontinuous Spectral Density Function Admissible Mapping 
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References

  1. 1.
    Donsker, M.D., Varadhan, S.R.S.: Asymptotic evaluation of certain Wiener integrals for large time. Functional Integration and its Applications, Proceedings of the International Conference held at the Cumberland Lodge, Windsor Great Park, London, in April 1974, A. M. Arthurs, (ed.). Oxford: Clarendon 1975Google Scholar
  2. 2.
    Donsker, M.D., Varadhan, S.R.S.: Asymptotic evaluation of certain Markov process expectations for large time, I. Commun. Pure Appl. Math. 28,1–47 (1976); II. Commun. Pure Appl. Math. 28, 279–301 (1975); III. Commun. Pure Appl. Math. 29, 389–461 (1976); IV. Commun. Pure Appl. Math. 36, 183–212 (1983)MathSciNetCrossRefGoogle Scholar
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    Donsker, M.D., Varadhan, S.R.S.: On laws of the iterated logarithm for local times. Commun. Pure Appl. Math. 30, 707–753 (1977)MathSciNetMATHCrossRefGoogle Scholar
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    Donsker, M.D., Varadhan, S.R.S.: Asymptotics for the Polaron. Commun. Pure Appl. Math. 36, 505–528 (1983)MathSciNetMATHCrossRefGoogle Scholar
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    Orey, S.: Large deviations and Shanon-McMillan theorems (preprint)Google Scholar

Copyright information

© Springer-Verlag Berlin, Heidelberg 1985

Authors and Affiliations

  • M. D. Donsker
    • 1
  • S. R. S. Varadhan
    • 1
  1. 1.Courant Institute of Mathematical SciencesNew York UniversityNew YorkUSA

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