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Lower functions for asymmetric Lévy processes
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  • Published: December 1990

Lower functions for asymmetric Lévy processes

  • In-Suk Wee1 

Probability Theory and Related Fields volume 85, pages 469–488 (1990)Cite this article

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Summary

Let {X t } be a ℝ1 process with stationary independent increments and its Lévy measurev be given byv{y∶y>x}=x −αL 1 (x), v{y∶y<−x}=x −αL 2 (x) whereL 1,L 2 are slowly varying at 0 and ∞ and 0<α≦1. We construct two types of a nondecreasing functionh(t) depending on 0<α<1 or α=1 such that lim inf\(\mathop {\sup }\limits_{0 \leqq s \leqq t} |X_S |/h(t) = C\) a.s. ast→ 0 andt→∞ for some positive finite constantC.

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References

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Author information

Authors and Affiliations

  1. Department of Mathematics, Korea University, Seoul, Korea

    In-Suk Wee

Authors
  1. In-Suk Wee
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Additional information

This research is partialy supported by a grant from Korea University

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Cite this article

Wee, IS. Lower functions for asymmetric Lévy processes. Probab. Th. Rel. Fields 85, 469–488 (1990). https://doi.org/10.1007/BF01203165

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  • Received: 22 September 1988

  • Revised: 15 November 1989

  • Issue Date: December 1990

  • DOI: https://doi.org/10.1007/BF01203165

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Keywords

  • Stochastic Process
  • Probability Theory
  • Mathematical Biology
  • Independent Increment
  • Lower Function
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