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The small-time Chung-Wichura law for Lévy processes with non-vanishing Brownian component
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  • Published: 11 December 2009

The small-time Chung-Wichura law for Lévy processes with non-vanishing Brownian component

  • Boris Buchmann1 &
  • Ross Maller2 

Probability Theory and Related Fields volume 149, pages 303–330 (2011)Cite this article

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  • 4 Citations

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Abstract

We give a “small time” functional version of Chung’s “other” law of the iterated logarithm for Lévy processes with non-vanishing Brownian component. This is an analogue of the “other” law of the iterated logarithm at “large times” for Lévy processes and random walks with finite variance, as extended to a functional version by Wichura. As one of many possible applications, we mention a functional law for a two-sided passage time process.

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Authors and Affiliations

  1. School of Mathematical Sciences, Monash University, Clayton Campus, Clayton, VIC, 3800, Australia

    Boris Buchmann

  2. Centre for Mathematics and its Applications, School of Finance and Applied Statistics, Australian National University, Canberra, ACT, Australia

    Ross Maller

Authors
  1. Boris Buchmann
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  2. Ross Maller
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Corresponding author

Correspondence to Boris Buchmann.

Additional information

This research was partially supported by ARC grants DP0664603 and DP0988483.

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Buchmann, B., Maller, R. The small-time Chung-Wichura law for Lévy processes with non-vanishing Brownian component. Probab. Theory Relat. Fields 149, 303–330 (2011). https://doi.org/10.1007/s00440-009-0255-1

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  • Received: 05 April 2009

  • Revised: 27 October 2009

  • Published: 11 December 2009

  • Issue Date: February 2011

  • DOI: https://doi.org/10.1007/s00440-009-0255-1

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Keywords

  • Lévy process
  • Local behaviour
  • Almost sure convergence
  • Iterated logarithm laws
  • Other law of the iterated logarithm
  • Cluster sets
  • Functional limit theorem

Mathematics Subject Classification (2000)

  • 60G51
  • 60F15
  • 60F17
  • 60F05
  • 60J65
  • 60J75
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