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On the Coupling of Dependent Random Variables and Applications

In: Empirical Process Techniques for Dependent Data

Author

Listed:
  • Florence Merlevède

    (Université Paris VI, L.S.T.A. Université Pierre et Marie Curie)

  • Magda Peligrad

    (University of Cincinnati, Department of Mathematical Sciences)

Abstract

In this paper we survey some results and further investigate the coupling of a sequence of dependent random variables with an independent one having the same marginal distributions. The upper bound of the distance between the variables with the same rank is given in terms of mixing coefficients. We shall apply the coupling methods to derive uniform laws of large numbers for the dependent random processes under various types of dependence. We shall also discuss the importance of coupling for obtaining the central limit theorem for strongly mixing sequences.

Suggested Citation

  • Florence Merlevède & Magda Peligrad, 2002. "On the Coupling of Dependent Random Variables and Applications," Springer Books, in: Herold Dehling & Thomas Mikosch & Michael Sørensen (ed.), Empirical Process Techniques for Dependent Data, pages 171-193, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-0099-4_5
    DOI: 10.1007/978-1-4612-0099-4_5
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