On Infinitely Divisible Distributions on Locally Compact Abelian Groups

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18 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)635-657
Number of pages23
JournalJournal of Theoretical Probability
Volume13
Issue number3
DOIs
Publication statusPublished - 2000 Jan 1
Externally publishedYes

Keywords

  • Semi-selfdecomposable distribution
  • Semistable law
  • Semistable process
  • i.i.d
  • p-adic field

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Statistics, Probability and Uncertainty

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