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Remarks on the central limit theorem for weakly dependent random variables

Part of the Lecture Notes in Mathematics book series (LNM,volume 1158)

Keywords

  • Central Limit Theorem
  • Invariance Principle
  • Dependent Random Variable
  • Martingale Difference
  • Martingale Approximation

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References

  1. Billingsley, P.: Convergence of Probability Measures, John Wiley and Sons, 1968.

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  2. Ibragimov, I.A.: A Central Limit Theorem for a class of dependent random variables, Theor.Prob.Appl.8, 83–89, 1963.

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  3. Gordin, M.I.: On the Central Limit Theorem for stationary processes. Soviet Math.Dokl., 10, 1174–1176, 1969.

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  4. Hall, P., Heyde, C.: Martingale limit theory and its application. Academic Press, New York, 1980.

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  5. Ibragimov, I.A.: A Note on the CLT for dependent random variables. Theor.Prob.Appl. 20, 135–140, 1975.

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  6. Ibragimov, Linnik: Independent and stationary sequences of random variables. Wolters Noordhoff Publishing, Groningen 1969.

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  7. Davydov, Y.A.: The invariance principle for stationary processes. Theor.Prob.Appl. 15, 487–498, 1970.

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  8. McLeish, D.L.: Invariance principles for dependent variables. Z.Wahrsch.verw.Gebiete, 32, 165–178, 1975.

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  9. Kipnis,C., Varadhan,S.R.S.: Central Limit Theorem for additive functionals of reversible Markov processes and application to simple exclusions: to appear in Comm.Math.Phys., 1985.

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© 1986 Springer-Verlag

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Dürr, D., Goldstein, S. (1986). Remarks on the central limit theorem for weakly dependent random variables. In: Albeverio, S.A., Blanchard, P., Streit, L. (eds) Stochastic Processes — Mathematics and Physics. Lecture Notes in Mathematics, vol 1158. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0080211

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  • DOI: https://doi.org/10.1007/BFb0080211

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15998-8

  • Online ISBN: 978-3-540-39703-8

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