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Small time two-sided LIL behavior for Lévy processes at zero
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  • Published: 27 March 2008

Small time two-sided LIL behavior for Lévy processes at zero

  • Mladen Savov1 

Probability Theory and Related Fields volume 144, pages 79–98 (2009)Cite this article

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Abstract

We wish to characterize when a Lévy process X t crosses boundaries b(t), in a two-sided sense, for small times t, where b(t) satisfies very mild conditions. An integral test is furnished for computing the value of sup t→0|X t |/b(t) = c. In some cases, we also specify a function b(t) in terms of the Lévy triplet, such that sup t→0 |X t |/b(t) = 1.

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Authors and Affiliations

  1. School of Mathematics, University of Manchester, Alan Turing Building, M13 9PL, Manchester, UK

    Mladen Savov

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  1. Mladen Savov
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Correspondence to Mladen Savov.

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Cite this article

Savov, M. Small time two-sided LIL behavior for Lévy processes at zero. Probab. Theory Relat. Fields 144, 79–98 (2009). https://doi.org/10.1007/s00440-008-0142-1

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  • Received: 01 October 2007

  • Revised: 25 January 2008

  • Published: 27 March 2008

  • Issue Date: May 2009

  • DOI: https://doi.org/10.1007/s00440-008-0142-1

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Keywords

  • Lévy process
  • LIL behavior
  • Norming functions
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