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

Paul Deheuvels and Pál Révész
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Paul Deheuvels: Université Paris VI
Pál Révész: Mathematical Institute Budapest and Technical University

A chapter in Mathematical Statistics and Probability Theory, 1987, pp 69-88 from Springer

Abstract: 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.

Keywords: Wiener Process; Empirical Process; BROWNIAN Bridge; Standard Wiener Process; Empirical Quantile (search for similar items in EconPapers)
Date: 1987
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-009-3963-9_7

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DOI: 10.1007/978-94-009-3963-9_7

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