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A lim inf result for the increments of the Wiener process under theL 2-norm
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  • Published: December 1995

A lim inf result for the increments of the Wiener process under theL 2-norm

  • K. Grill1 

Probability Theory and Related Fields volume 102, pages 567–573 (1995)Cite this article

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Summary

We prove an almost sure lower limit law for the square integral of the large increments of the Wiener process, extending results obtained by Li (1992).

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References

  1. Anderson, T.W.: The integral of a symmetric unimodal function over a symmetric convex set and some probability inequalities. Proc. Am. Math. Soc.6, 170–176 (1955)

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  2. Anderson, T.W., Darling, D.A.: Asymptotic theory of certain “goodness of fit” criteria based on stochastic processes. Ann. Math. Statist.23, 193–212 (1952)

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  3. Grill, K.: On the increments of the Wiener process. Stud. Sci. Math. Hung.26, 329–354 (1991)

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  4. Li, W.V.: Lim inf results for the Wiener process and its increments under theL 2-norm. Probab. Theory Relat. Fields92, 69–90 (1992)

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Author information

Authors and Affiliations

  1. Institut für Statistik und Wahrscheinlichkeitstheorie, TU Wien, Wiedner Hauptstrasse 8-10, A-1040, Vienna, Austria

    K. Grill

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  1. K. Grill
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Additional information

Work supported by an NSERC Foreign Researcher Award at Carleton University

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Cite this article

Grill, K. A lim inf result for the increments of the Wiener process under theL 2-norm. Probab. Th. Rel. Fields 102, 567–573 (1995). https://doi.org/10.1007/BF01198850

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  • Received: 31 August 1994

  • Revised: 14 March 1995

  • Issue Date: December 1995

  • DOI: https://doi.org/10.1007/BF01198850

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Mathematics Subject Classification

  • 60F15
  • 60J65
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