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A Characterization of Small and Large Time Limit Laws for Self-normalized Lévy Processes

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Limit Theorems in Probability, Statistics and Number Theory

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 42))

Abstract

We establish asymptotic distribution results for self-normalized Lévy processes at small and large times that are analogs of those of Chistyakov and Götze [Ann. Probab. 32:28–77, 2004] for self-normalized sums.

AMS 2000 Subject Classifications: 60F05, 60F17, 60G51.

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Acknowledgements

Research of Ross Maller was partially supported by ARC Grant DP1092502. Research of David M. Mason was partially supported by NSF Grant DMS–0503908.

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Authors and Affiliations

  1. Centre for Mathematical Analysis, Mathematical Sciences Institute, Australian National University, Canberra, ACT, Australia

    Ross Maller

  2. Department of Applied Economics and Statistics, 213 Townsend Hall, Newark, DE, 19716, USA

    David M. Mason

Authors
  1. Ross Maller
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  2. David M. Mason
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Corresponding author

Correspondence to David M. Mason .

Editor information

Editors and Affiliations

  1. Mathematics Faculty, Ruhr-University Bochum, Universitätstr. 150, Bochum, 44780, Germany

    Peter Eichelsbacher

  2. Mathematics Faculty, University of Bielefeld, Universitätsstr. 25, Bielefeld, 33615, Germany

    Guido Elsner

  3. Mathematics Faculty, University of Bielefeld, Universitätsstr. 25, Bielefeld, 33615, Germany

    Holger Kösters

  4. Institute for Mathematical Statistics, University of Münster, Einsteinstrasse 62, Münster, 48149, Germany

    Matthias Löwe

  5. Mathematics Institute, University of München, Theresienstr. 39, München, 80333, Germany

    Franz Merkl

  6. Centre for Mathematics, Technische Universität München, Boltzmannstr. 3, Garching bei München, 85747, Germany

    Silke Rolles

Additional information

Dedicated to Friedrich Götze on the occasion of his sixtieth birthday.

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Maller, R., Mason, D.M. (2013). A Characterization of Small and Large Time Limit Laws for Self-normalized Lévy Processes. In: Eichelsbacher, P., Elsner, G., Kösters, H., Löwe, M., Merkl, F., Rolles, S. (eds) Limit Theorems in Probability, Statistics and Number Theory. Springer Proceedings in Mathematics & Statistics, vol 42. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36068-8_8

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