A subclass of type G selfdecomposable distributions on ℝd

Takahiro Aoyama; Makoto Maejima; Jan Rosiński

doi:10.1007/s10959-007-0129-3

A subclass of type G selfdecomposable distributions on ℝ^d

Takahiro Aoyama, Makoto Maejima, Jan Rosiński

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

18 Citations (Scopus)

Abstract

A new class of type G selfdecomposable distributions on ℝ^d 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 language	English
Pages (from-to)	14-34
Number of pages	21
Journal	Journal of Theoretical Probability
Volume	21
Issue number	1
DOIs	https://doi.org/10.1007/s10959-007-0129-3
Publication status	Published - Mar 2008
Externally published	Yes

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

Access to Document

10.1007/s10959-007-0129-3

Cite this

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abstract = "A new class of type G selfdecomposable distributions on ℝd is introduced and characterized in terms of stochastic integrals with respect to L{\'e}vy 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.",

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author = "Takahiro Aoyama and Makoto Maejima and Jan Rosi{\'n}ski",

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KW - Type G distribution

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