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Weak Laws for the Increments of Wiener Processes, Brownian Bridges Empirical Processes and Partial Sums of I.I.D.R.V.’S

In: Mathematical Statistics and Probability Theory

Author

Listed:
  • Paul Deheuvels

    (Université Paris VI)

  • Pál Révész

    (Mathematical Institute Budapest and Technical University)

Abstract

We obtain the limiting asymptotic distributions of the moduli of continuity of the Wiener process and Brownian bridge. We apply these results via strong invariance principles to evaluate the limiting behavior of increments of partial sums of independent and identically distributed random variables, and also of the moduli of continuity of empirical and quantile processes for a uniform distribution. We complete these results in the range not covered by invariance principles.

Suggested Citation

  • Paul Deheuvels & Pál Révész, 1987. "Weak Laws for the Increments of Wiener Processes, Brownian Bridges Empirical Processes and Partial Sums of I.I.D.R.V.’S," Springer Books, in: M. L. Puri & P. Révész & W. Wertz (ed.), Mathematical Statistics and Probability Theory, pages 69-88, Springer.
    • Handle: RePEc:spr:sprchp:978-94-009-3963-9_7
    DOI: 10.1007/978-94-009-3963-9_7
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