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Lower functions for processes with stationary independent increments
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  • Published: December 1988

Lower functions for processes with stationary independent increments

  • In-Suk Wee1 

Probability Theory and Related Fields volume 77, pages 551–566 (1988)Cite this article

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Summary

Let {X t } be aR 1-valued process with stationary independent increments and\(A_t = \mathop {\sup }\limits_{s \leqq t} |X_s |\). In this paper we find a sufficient condition for there to exist nonnegative and nondecreasing functionh(t) such that lim infA t /h(t)=C a.s. ast→0 andt→∞, for some positive finite constantC whenh(t) takes a particular form. Also two analytic conditions are considered as application.

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References

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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 partially supported by Korea Science & Engineering Foundation

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Cite this article

Wee, IS. Lower functions for processes with stationary independent increments. Probab. Th. Rel. Fields 77, 551–566 (1988). https://doi.org/10.1007/BF00959617

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  • Received: 15 June 1985

  • Revised: 20 October 1987

  • Issue Date: December 1988

  • DOI: https://doi.org/10.1007/BF00959617

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Keywords

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