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On the joint distribution of ladder variables of random walk
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  • Published: December 1993

On the joint distribution of ladder variables of random walk

  • R. A. Doney1 &
  • P. E. Greenwood2 

Probability Theory and Related Fields volume 94, pages 457–472 (1993)Cite this article

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  • 13 Citations

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Summary

The ladder timeN and ladder heightH of a random walk {S n ,n≧1} as a pair (N, H) lie in the domain of attraction of a bivariate stable law ifS 1 is in a domain of attraction, as was shown by Greenwood et al. (1982). In this paper we prove a converse. IfP(S n >0) converges and (N, H) lies in a bivariate domain of attraction thenS 1 is also in a domain of attraction.

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Authors and Affiliations

  1. Department of Mathematics, University of Manchester, M13 9PL, Manchester, UK

    R. A. Doney

  2. Department of Mathematics, University of British Columbia, V6T 1Y4, Vancouver, B.C., Canada

    P. E. Greenwood

Authors
  1. R. A. Doney
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  2. P. E. Greenwood
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Doney, R.A., Greenwood, P.E. On the joint distribution of ladder variables of random walk. Probab. Th. Rel. Fields 94, 457–472 (1993). https://doi.org/10.1007/BF01192558

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  • Received: 07 February 1991

  • Revised: 20 May 1992

  • Issue Date: December 1993

  • DOI: https://doi.org/10.1007/BF01192558

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Keywords

  • Stochastic Process
  • Random Walk
  • Probability Theory
  • Mathematical Biology
  • Joint Distribution
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