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Absolute continuity of some semi-selfdecomposable distributions and self-similar measures
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  • Published: July 2000

Absolute continuity of some semi-selfdecomposable distributions and self-similar measures

  • Toshiro Watanabe1 

Probability Theory and Related Fields volume 117, pages 387–405 (2000)Cite this article

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  • 12 Citations

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Abstract.

P.S. numbers are introduced in relation to absolute continuity of some infinite Bernoulli convolutions. Absolute continuity and continuous singularity of some semi-selfdecomposable distributions are studied as marginal distributions of subordinators. It is shown that these properties are widely different according as their spans are P.V. numbers or the reciprocals of P.S. numbers. A simple example of a subordinator whose distribution is continuous singular for small time and absolutely continuous for large time is given. Absolute continuity of convolutions of multidimensional homogeneous self-similar measures are also discussed.

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Authors and Affiliations

  1. Center for Mathematical Sciences, The University of Aizu, Aizu-Wakamatsu, Fukushima 965-8580, Japan. e-mail: t-watanb@u-aizu.ac.jp, , , , , , JP

    Toshiro Watanabe

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  1. Toshiro Watanabe
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Received: 27 December 1998 / Revised version: 20 August 1999 / Published online: 31 May 2000

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Watanabe, T. Absolute continuity of some semi-selfdecomposable distributions and self-similar measures. Probab Theory Relat Fields 117, 387–405 (2000). https://doi.org/10.1007/s004400050011

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  • Issue Date: July 2000

  • DOI: https://doi.org/10.1007/s004400050011

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  • Mathematics Subject Classification (1991): 60E07, 60J30, 28A80
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