A subclass of type G selfdecomposable distributions on ℝd

Takahiro Aoyama, Makoto Maejima, Jan Rosiński

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)

Abstract

A new class of type G selfdecomposable distributions on ℝd is introduced and characterized in terms of stochastic integrals with respect to Lévy processes. This class is a strict subclass of the class of type G and selfdecomposable distributions, and in dimension one, it is strictly bigger than the class of variance mixtures of normal distributions by selfdecomposable distributions. The relation to several other known classes of infinitely divisible distributions is established.

Original languageEnglish
Pages (from-to)14-34
Number of pages21
JournalJournal of Theoretical Probability
Volume21
Issue number1
DOIs
Publication statusPublished - Mar 1 2008
Externally publishedYes

Keywords

  • Infinitely divisible distribution
  • Selfdecomposable distribution
  • Stochastic integral with respect to Lévy process
  • Type G distribution

ASJC Scopus subject areas

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

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