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Exponential convergence under mixing
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  • Published: June 1989

Exponential convergence under mixing

  • Roberto H. Schonmann1 nAff2 

Probability Theory and Related Fields volume 81, pages 235–238 (1989)Cite this article

Summary

We show that for a ϕ-mixing stationary sequence of bounded random variables, the average of the firstn variables converges exponentially fast withn to the mean value of these random variables.

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References

  1. Chernoff, H.: A measure of asymptotic efficiency for tests of hypothesis based on sums of observations. Ann. Math. Stat.23, 493–507 (1952)

    Google Scholar 

  2. Cramer, H.: Sur un nouveau théorèm limite de la théorie des probabilités. Colloqium on theory of probability. Paris: Hermann (1937)

    Google Scholar 

  3. Dürr, D., Goldstein, S.: Remarks on the central limit theorem for weakly dependent random variables. In: Dolb, A., Eckmann, B. (eds.) Stochastic processes, mathematics and physics. Lect. Notes Math. Vol. 1158, pp. 104–118. Berlin Heidelberg: Springer 1958

    Google Scholar 

  4. Grimmett, G.: Large deviations in subadditive processes and first passage percolation. In: Durrett, R. (ed.) Particle systems, random media and large deviations. Contemp. Math., Vol. 41. pp. 175–194. Providence: AMS 1985

    Google Scholar 

  5. Ibragimov, I.A., Linnik, Yu.V.: Independent and stationary sequences of random variables. Groningen: Noordhoff 1969

    Google Scholar 

  6. Lebowitz, J.L., Schonmann, R.H.: Pseudo free energies and large deviations for non-Gibbsian FKG measures. Probab. Th. Rel. Fields77, 49–64 (1988)

    Google Scholar 

  7. Rosenblatt, M.: Dependence and asymptotic independence for random processes. In: Rosenblatt, M. (ed.) Studies in Probability Theory, MAA Studies in Mathematics, vol. 18, pp. 24–45 1978

  8. Schonmann, R.H.: Second order large deviation estimates for ferromagnetic systems in the phase coexistence region. Commun. Math. Phys.112, 409–422 (1987)

    Google Scholar 

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Author information

Author notes
  1. Roberto H. Schonmann

    Present address: São Paulo University, Brazil

Authors and Affiliations

  1. Instituto de Matemática e Estatística, USP, Caixa Postal 20570, São Paulo, SP, Brasil

    Roberto H. Schonmann

Authors
  1. Roberto H. Schonmann
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Additional information

Work supported by the U.S. Army Research Office through the Mathematical Sciences Institute at Cornell and a NSF Grant to Cornell University

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Cite this article

Schonmann, R.H. Exponential convergence under mixing. Probab. Th. Rel. Fields 81, 235–238 (1989). https://doi.org/10.1007/BF00319552

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  • Received: 16 December 1987

  • Issue Date: June 1989

  • DOI: https://doi.org/10.1007/BF00319552

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Keywords

  • Stochastic Process
  • Probability Theory
  • Mathematical Biology
  • Stationary Sequence
  • Exponential Convergence
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