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Iterated Logarithm Laws for the Square Integral of a Wiener Process

  • Conference paper
The First Pannonian Symposium on Mathematical Statistics

Part of the book series: Lecture Notes in Statistics ((LNS,volume 8))

Abstract

Consider a standard Wiener process w(t), t≥o, w(o)=o and its square integral

$$I(T) = \int\limits_0^T {{w^2}(t)} dt.$$

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References

  1. Cameron, R.H. and Martin, W.T., The Wiener measure of Hilbert neighborhoods in the space of real continuous functions, J.Math. Phys. 23 (1944), 195–209.

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  2. Donsker, M.D. and Varadhan, S.R.S., On laws of the iterated logarithm for local times, Comm.Pure Appl. Math. 30 (1977), 707–753.

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  4. RÉvÉsz, P., A note to the Chung — ErdÕs — Sirao theorem, to appear.

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  5. [5] Strassen, V., An invariance principle for the law of the iterated logarithm, Z. Wahrscheinlichkeitstheorie verw. Gebiete 3 (1964), 211–226.

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Author information

Authors and Affiliations

  1. Mathematical Institute of Hung. Acad. Sci., Reåltanoda u. 13-15, Budapest, Hungary, H-1053

    Endre Csåki

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  1. Endre Csåki
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© 1981 Springer-Verlag New York Inc.

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Csåki, E. (1981). Iterated Logarithm Laws for the Square Integral of a Wiener Process. In: The First Pannonian Symposium on Mathematical Statistics. Lecture Notes in Statistics, vol 8. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-5934-3_6

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  • DOI: https://doi.org/10.1007/978-1-4612-5934-3_6

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-90583-9

  • Online ISBN: 978-1-4612-5934-3

  • eBook Packages: Springer Book Archive

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