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Strong and conditional invariance principles for samples attracted to stable laws
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  • Published: June 1997

Strong and conditional invariance principles for samples attracted to stable laws

  • Raoul LePage1,
  • Krzysztof Podgórski2 &
  • Michał Ryznar3 

Probability Theory and Related Fields volume 108, pages 281–298 (1997)Cite this article

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  • 12 Citations

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Summary.

We prove almost sure convergence of a representation of normalized partial sum processes of a sequence of i.i.d. random variables from the domain of attraction of an α-stable law, α<2. We obtain an explicit form of the limit in terms of the LePage series representation of stable laws. One consequence of these results is a conditional invariance principle having applications to option pricing as well as to resampling by signs and permutations.

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Authors and Affiliations

  1. Department of Probability and Statistics, Michigan State University, East Lansing, MI 48823, USA. E-mail: entropy@msu.edu, , , , , , US

    Raoul LePage

  2. Department of Mathematical Sciences, IUPUI, Indianapolis, IN 46202-3216, USA. E-mail: kpodgorski@math.iupui.edu, , , , , , IN

    Krzysztof Podgórski

  3. Institute of Mathematics, Technical University of Wroclaw, 50-370 Wroclaw, POLAND E-mail: ryznar@graf.im.pwr.wroc.p1, , , , , , PL

    Michał Ryznar

Authors
  1. Raoul LePage
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  2. Krzysztof Podgórski
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  3. Michał Ryznar
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Received: 11 April 1994 / In revised form: 5 November 1996

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LePage, R., Podgórski, K. & Ryznar, M. Strong and conditional invariance principles for samples attracted to stable laws. Probab Theory Relat Fields 108, 281–298 (1997). https://doi.org/10.1007/s004400050110

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  • Issue Date: June 1997

  • DOI: https://doi.org/10.1007/s004400050110

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  • Mathematics Subject Classification (1991): 60E07
  • 60F17; Secondary 60F15
  • 60G50
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