A note on self-decomposability of stable process subordinated to self-decomposable subordinator

descriptionPublicationkeyboard_double_arrow_right Article 01 Jul 2005 English Publisher:Elsevier BVJournal:Statistics & Probability Letters, volume 74, pages 89-91 (issn: 0167-7152,

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Authors: Kozubowski, Tomasz J.;

doi: 10.1016/j.spl.2005.04.025 , 10.1016/j.spl.2005.04.011

A note on self-decomposability of stable process subordinated to self-decomposable subordinator

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Abstract

By aid of an example the author proves the following theorem: There is self-decomposable subordinator \({T(t), t\geq 0}\), and a stable Lévy motion \({X(t), t\geq 0}\), such that the subordinated process \({Y(t)} = {X(T(t)), t \geq 0}\), is not self-decomposable. Then by three remarks the author illuminates this result.

Related Organizations

University of Nevada Reno
United States

Keywords

Stable stochastic processes, unimodality, Continuous-time Markov processes on general state spaces, subordination, geometric stable law, Linnik distribution

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