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

  • Ross Maller
  • David M. MasonEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 42)


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.


Domain of Attraction of Normal Distribution Large Times Lévy Process Quadratic Variation Self-Normalized Small Times Stable Laws 



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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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Centre for Mathematical Analysis, Mathematical Sciences InstituteAustralian National UniversityCanberraAustralia
  2. 2.Department of Applied Economics and StatisticsNewarkUSA

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