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On a Zero-One Law for the Norm Process of Transient Random Walk

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Séminaire de Probabilités XLIII

Part of the book series: Lecture Notes in Mathematics ((SEMPROBAB,volume 2006))

Abstract

A zero-one law of Engelbert–Schmidt type is proven for the norm process of a transient random walk. An invariance principle for random walk local times and a limit version of Jeulin’s lemma play key roles.

AMS 2000 Subject class: Primary 60G50; Secondary 60F20, 60J55

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Acknowledgements

The authors would like to thank Professor Tokuzo Shiga who kindly allowed them to append to this paper his detailed study (Shiga, unpublished) about Jeulin’s lemma. They also thank Professors Marc Yor, Katsushi Fukuyama and Patrick J. Fitzsimmons for valuable comments. They are thankful to the referee for pointing out several errors in the earlier version. The first author, Ayako Matsumoto, expresses her sincerest gratitudes to Professors Yasunari Higuchi and Taizo Chiyonobu for their encouraging guidance in her study of mathematics. The research of the second author, Kouji Yano, was supported by KAKENHI (20740060).

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Authors and Affiliations

  1. T & D Financial Life Insurance Company, Tokyo, Japan

    Ayako Matsumoto

  2. Graduate School of Science, Kobe University, Kobe, Japan

    Kouji Yano

Authors
  1. Ayako Matsumoto
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  2. Kouji Yano
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Correspondence to Kouji Yano .

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Editors and Affiliations

  1. Lab. de Probabilités et Modèles Aléatoir, Université Pierre et Marie Curie, place Jussieu 4, Paris Cedex 05, 75252, France

    Catherine Donati-Martin

  2. IECN, Campus scientifique, BP 239, Nancy-Université, INRIA, Vandoeuvre-lès-Nancy, 54506, France

    Antoine Lejay

  3. Laboratoire de Mathématiques, Université de Versailles-St-Quentin, avenue des Etats-Unis 45, Versailles, 78035, France

    Alain Rouault

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Matsumoto, A., Yano, K. (2011). On a Zero-One Law for the Norm Process of Transient Random Walk. In: Donati-Martin, C., Lejay, A., Rouault, A. (eds) Séminaire de Probabilités XLIII. Lecture Notes in Mathematics(), vol 2006. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15217-7_4

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