Characterizations of subclasses of type G distributions on ℝRd by stochastic integral representations

Takahiro Aoyama; Makoto Maejima

doi:10.3150/07-BEJ5136

Characterizations of subclasses of type G distributions on ℝR^d by stochastic integral representations

Takahiro Aoyama, Makoto Maejima

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

Abstract

The class of type G distributions on ℝ^d and its nested subclasses are studied. An analytic characterization in terms of Lévy measures for the class of type G distributions is known. In this paper, probabilistic characterizations by stochastic integral representations for all classes are shown, and analytic characterizations for the nested subclasses are given in terms of Lévy measures.

Original language	English
Pages (from-to)	148-160
Number of pages	13
Journal	Bernoulli
Volume	13
Issue number	1
DOIs	https://doi.org/10.3150/07-BEJ5136
Publication status	Published - 2007
Externally published	Yes

Keywords

Infinitely divisible distribution on ℝR
Lévy process
Stochastic integral representation
Type G distribution

ASJC Scopus subject areas

Statistics and Probability

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abstract = "The class of type G distributions on ℝd and its nested subclasses are studied. An analytic characterization in terms of L{\'e}vy measures for the class of type G distributions is known. In this paper, probabilistic characterizations by stochastic integral representations for all classes are shown, and analytic characterizations for the nested subclasses are given in terms of L{\'e}vy measures.",

keywords = "Infinitely divisible distribution on ℝR, L{\'e}vy process, Stochastic integral representation, Type G distribution",

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