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The large deviation principle for hypermixing processes
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  • Published: August 1988

The large deviation principle for hypermixing processes

  • T. Chiyonobu1 &
  • S. Kusuoka2 

Probability Theory and Related Fields volume 78, pages 627–649 (1988)Cite this article

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  • 17 Citations

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Summary

The large deviation principle of Donsker and Varadhan type is proved under certain hypotheses on the base stationary process. Some examples of processes satisfying those hypotheses are also given.

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References

  1. Accardi, L., Olla, S.: Donsker and Varadhan's theory for stationary processes. (Preprint)

  2. Donsker, M.D., Varadhan, S.R.S.: Asymptotic evaluation of certain Markov process expectations for large time, IV. Commun. Pure Appl. Math. 36, 183–212 (1983)

    Google Scholar 

  3. Donsker, M.D., Varadhan, S.R.S.: Large deviations for stationary Gaussian processes. Commun. Math. Phys. 97, 187–210 (1985)

    Google Scholar 

  4. Guerra, F., Rosen, L., Simon, B.: The P(φ)2 Euclidean quantum field theory as classical statistical mechanics, Ann. Math. 101, 111–259 (1975)

    Google Scholar 

  5. Kesten, H., Papanicolaou, G.C.: A limit theorem for turbulent diffusion. Commun. Math. Phys. 65, 97–138 (1979)

    Google Scholar 

  6. Kusuoka, S.: The variational principle for stationary Guassian Markov fields. Theory and Application of Random Fields, Proc. of the IFIP-WG 7/1 Working Conference, Bangalore, India, 1982 (Lecture Notes Control Inf. Sci., vol. 49, pp. 179–187) Berlin Heidelberg New York: Springer 1983

    Google Scholar 

  7. Nelson, E.: The free Markov field, J. Funct. Anal. 12, 211–227 (1973)

    Google Scholar 

  8. Olla, S.: Large deviation for almost Markovian processes. Probab. Th. Rel. Fields 76, 395–409 (1987)

    Google Scholar 

  9. Orey, S.: On the Shannon-Perez-Moy theorem. Proc. on Particle systems, random media, and large deviations (Brunswick, Maine, 1984). Contemp. Math. 41, 319–327 (1985)

    Google Scholar 

  10. Rozanov, Yu.A.: Stationary random processes. San Francisco: Holden-Day 1967

    Google Scholar 

  11. Simon, B.: The P(φ)2 Eclidean (quantum) field theory. Princeton: Princeton University Press 1974

    Google Scholar 

  12. Stroock, D.: An introduction to the theory of large deviations. Berlin Heidelberg New York: Springer 1984

    Google Scholar 

  13. Takahashi, Y.: Entropy functional (free energy) for dynamical systems and their random perturbations, Proc. Taniguchi Symp. on Stoc. Anal. at Katata and Kyoto. Tokyo: Kinokuniya North Holland 1982

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Nagoya University, 464, Nagoya, Japan

    T. Chiyonobu

  2. Research Institute for Mathematical Science, Kyoto University, 606, Kyoto, Japan

    S. Kusuoka

Authors
  1. T. Chiyonobu
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  2. S. Kusuoka
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Cite this article

Chiyonobu, T., Kusuoka, S. The large deviation principle for hypermixing processes. Probab. Th. Rel. Fields 78, 627–649 (1988). https://doi.org/10.1007/BF00353880

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  • Received: 09 September 1987

  • Issue Date: August 1988

  • DOI: https://doi.org/10.1007/BF00353880

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Keywords

  • Stochastic Process
  • Stationary Process
  • Probability Theory
  • Statistical Theory
  • Deviation Principle
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