On Infinitely Divisible Distributions on Locally Compact Abelian Groups

Kumi Yasuda ()
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Kumi Yasuda: Kyushu University

Journal of Theoretical Probability, 2000, vol. 13, issue 3, 635-657

Abstract: 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.

Keywords: semi-selfdecomposable distribution; semistable law; semistable process; i.i.d.; p-adic field (search for similar items in EconPapers)
Date: 2000
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Citations: View citations in EconPapers (3)

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DOI: 10.1023/A:1007850210027

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