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Spitzer's condition and ladder variables in random walks
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  • Published: December 1995

Spitzer's condition and ladder variables in random walks

  • R. A. Doney1 

Probability Theory and Related Fields volume 101, pages 577–580 (1995)Cite this article

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Summary

Spitzer's condition holds for a random walk if the probabilities ρ n =P{ n > 0} converge in Cèsaro mean to ϱ, where 0<ϱ<1. We answer a question which was posed both by Spitzer [12] and by Emery [5] by showing that whenever this happens, it is actually true that ρn converges to ϱ. This also enables us to give an improved version of a result in Doney and Greenwood [4], and show that the random walk is in a domain of attraction, without centering, if and only if the first ladder epoch and height are in a bivariate domain of attraction.

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References

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Authors and Affiliations

  1. Statistical Laboratory, Department of Mathematics, University of Manchester, Oxford Road, M13 9PL, Manchester, UK

    R. A. Doney

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  1. R. A. Doney
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Doney, R.A. Spitzer's condition and ladder variables in random walks. Probab. Th. Rel. Fields 101, 577–580 (1995). https://doi.org/10.1007/BF01202785

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  • Received: 04 August 1994

  • Revised: 16 November 1994

  • Issue Date: December 1995

  • DOI: https://doi.org/10.1007/BF01202785

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Mathematics Subject Classification (1991)

  • 60J15
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