Geometric stable and semistable distributions on Z+d

• Autorzy: Bouzar N.
• Języki publikacji: EN

Abstrakty

EN

The aim of this article is to study geometric F-semistable and geometric F-stable distributions on the d-dimensional lattice Z^d₊. We obtain several properties for these distributions, including characterizations in terms of their probability generating functions.We describe a relation between geometric F-semistability and geometric F-stability and their counterparts on R^d₊ and, as a consequence, we derive some mixture representations and construct some examples.We establish limit theorems and discuss the related concepts of complete and partial geometric attraction for distributions on Z^d₊. As an application, we derive the marginal distribution of the innovation sequence of a Z^d₊-valued stationary autoregressive proces of order p with a geometric F-stable marginal distribution.

Słowa kluczowe

EN

semigroup; geometric infinite divisibility; branching processes; mixture representation; domain of geometric attraction

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2015
• Tom: Vol. 35, Fasc. 2
• Strony: 223--245
• Opis fizyczny: Bibliogr. 24 poz.

Twórcy

autor

Bouzar N.

• University of Indianapolis, Department of Mathematics and Computer Science, 1400 E. Hanna Ave., Indianapolis, IN 46227, USA

Bibliografia

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Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).