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Asymptotic expansions for renewal measures in the plane
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  • Published: December 1988

Asymptotic expansions for renewal measures in the plane

  • Robert Keener1 

Probability Theory and Related Fields volume 80, pages 1–20 (1988)Cite this article

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Summary

Let P be a distribution in the plane and define the renewal measure R=ΣP *nwhere * denotes convolution. The main results of this paper are three term asymptotic expansions for R far from the origin. As an application, expansions are obtained for distributions in linear boundary crossing problems.

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References

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Author information

Authors and Affiliations

  1. Department of Statistics, University of Michigan, 1444 Mason Hall, 48109, Ann Arbor, MI, USA

    Robert Keener

Authors
  1. Robert Keener
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Additional information

Research supported by NSF grants MCS-8102080 and DMS-8504708

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Cite this article

Keener, R. Asymptotic expansions for renewal measures in the plane. Probab. Th. Rel. Fields 80, 1–20 (1988). https://doi.org/10.1007/BF00348749

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  • Received: 10 April 1986

  • Revised: 20 April 1988

  • Issue Date: December 1988

  • DOI: https://doi.org/10.1007/BF00348749

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Keywords

  • Stochastic Process
  • Convolution
  • Probability Theory
  • Asymptotic Expansion
  • Statistical Theory
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