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On Infinitely Divisible Distributions on Locally Compact Abelian Groups

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  • Kumi Yasuda

    (Kyushu University)

Abstract

Our aim in this paper is to characterize some classes of infinitely divisible distributions on locally compact abelian groups. Firstly infinitely divisible distributions with no idempotent factor on locally compact abelian groups are characterized by means of limit distributions of sums of independent random variables. We introduce semi-selfdecomposable distributions on topological fields, and in case of totally disconnected fields we give a limit theorem for them. We also give a characterization of semistable laws on p-adic field and show that semistable processes are constructed as scaling limits of sums of i.i.d.

Suggested Citation

  • Kumi Yasuda, 2000. "On Infinitely Divisible Distributions on Locally Compact Abelian Groups," Journal of Theoretical Probability, Springer, vol. 13(3), pages 635-657, July.
    • Handle: RePEc:spr:jotpro:v:13:y:2000:i:3:d:10.1023_a:1007850210027
    DOI: 10.1023/A:1007850210027
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    References listed on IDEAS

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    1. Albeverio, Sergio & Karwowski, Witold, 1994. "A random walk on p-adics--the generator and its spectrum," Stochastic Processes and their Applications, Elsevier, vol. 53(1), pages 1-22, September.
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    Cited by:

    1. Kumi Yasuda, 2020. "Large Deviations for Scaled Sums of p-Adic-Valued Rotation-Symmetric Independent and Identically Distributed Random Variables," Journal of Theoretical Probability, Springer, vol. 33(2), pages 1196-1210, June.
    2. Makoto Maejima & Riddhi Shah, 2006. "Moments and Projections of Semistable Probability Measures on p-adic Vector Spaces," Journal of Theoretical Probability, Springer, vol. 19(2), pages 447-459, June.
    3. Hiroshi Kaneko & Xuelei Zhao, 2006. "Transition Semi–groups on a Local Field Induced by Galois Group and their Representation," Journal of Theoretical Probability, Springer, vol. 19(1), pages 221-234, January.

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