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On harmonic renewal measures
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  • Published: September 1986

On harmonic renewal measures

  • Rudolf Grübel1 

Probability Theory and Related Fields volume 71, pages 393–404 (1986)Cite this article

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Summary

Let μ be a probability and\(\nu _h = \sum\limits_{n = 1}^\infty {\frac{1}{n}\mu ^{*n} }\) the corresponding harmonic renewal measure. Complementing earlier results where μ is concentrated on a halfline we investigate the behaviour ofv h ([x, x + 1]) and the harmonic renewal functionG(x) =v h((−∞,x])asx→∞ ifm 1=∫xμ(dx)>0. We also consider the casem 1=0.

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Authors and Affiliations

  1. Department of Mathematics, Imperial College, 180 Queen's Gate, SW7 2BZ, London, England

    Rudolf Grübel

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  1. Rudolf Grübel
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Grübel, R. On harmonic renewal measures. Probab. Th. Rel. Fields 71, 393–404 (1986). https://doi.org/10.1007/BF01000213

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  • Received: 30 November 1984

  • Revised: 10 July 1985

  • Issue Date: September 1986

  • DOI: https://doi.org/10.1007/BF01000213

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Keywords

  • Stochastic Process
  • Probability Theory
  • Early Result
  • Mathematical Biology
  • Renewal Measure
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