A characterization of subclasses of semi-selfdecomposable distributions by stochastic integral representations

Maejima, Makoto; Miura, Manabu

doi:10.1016/j.spl.2006.12.004

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“…Maejima and Ueda [12] established the representation (1.2) for distributions in SSD α (R d ) and extended it to distributions in nested subclasses of SSD α (R d ). Maejima and Miura [10] obtained a stochastic integral representation for distributions in SSD α (R d ) similar to (1.1) but where the integration was with respect to a semi-Lévy process.…”

Section: Introductionmentioning

confidence: 99%

Stochastic integral representations of F-selfdecomposable and F-semi-selfdecomposable distributions

Bouzar¹

2016

COSA

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We study two specific mappings defined on the class of infinitely divisible distributions on Z + with finite log-moments. As a consequence, we re-derive some known stochastic integral representations for Fselfdecomposable distributions and obtain some new ones for F-semi-selfdecomposable distributions. Stochastic integral representations for discrete distributions in nested subclasses of F-selfdecomposable and F-semi-selfdecomposable distributions are established via the iterates of the aforementioned mappings.

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Section: Introductionmentioning

confidence: 99%