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On the Weak Invariance Principle for Stationary Sequences under Projective Criteria

Author

Listed:
  • Florence Merlevède

    (Université Paris VI, et C.N.R.S UMR 7599)

  • Magda Peligrad

    (University of Cincinnati)

Abstract

In this paper, we study the central limit theorem and its weak invariance principle for sums of a stationary sequence of random variables, via a martingale decomposition. Our conditions involve the conditional expectation of sums of random variables with respect to the distant past. The results contribute to the clarification of the central limit question for stationary sequences.

Suggested Citation

  • Florence Merlevède & Magda Peligrad, 2006. "On the Weak Invariance Principle for Stationary Sequences under Projective Criteria," Journal of Theoretical Probability, Springer, vol. 19(3), pages 647-689, December.
    • Handle: RePEc:spr:jotpro:v:19:y:2006:i:3:d:10.1007_s10959-006-0029-y
    DOI: 10.1007/s10959-006-0029-y
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    References listed on IDEAS

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    1. Shao, Qi-Man, 1993. "Almost sure invariance principles for mixing sequences of random variables," Stochastic Processes and their Applications, Elsevier, vol. 48(2), pages 319-334, November.
    2. Dedecker, Jérôme & Doukhan, Paul, 2003. "A new covariance inequality and applications," Stochastic Processes and their Applications, Elsevier, vol. 106(1), pages 63-80, July.
    3. Richard C. Bradley, 1997. "On Quantiles and the Central Limit Question for Strongly Mixing Sequences," Journal of Theoretical Probability, Springer, vol. 10(2), pages 507-555, April.
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    Cited by:

    1. Jérôme Dedecker & Florence Merlevède & Dalibor Volný, 2007. "On the Weak Invariance Principle for Non-Adapted Sequences under Projective Criteria," Journal of Theoretical Probability, Springer, vol. 20(4), pages 971-1004, December.
    2. Yizao Wang, 2014. "An Invariance Principle for Fractional Brownian Sheets," Journal of Theoretical Probability, Springer, vol. 27(4), pages 1124-1139, December.

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