Series representation of time-stable stochastic processes
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BORIS DOI
Date of Publication
2018
Publication Type
Article
Division/Institute
Author
Subject(s)
Series
Probability and mathematical statistics
ISSN or ISBN (if monograph)
0208-4147
Publisher
Kazimierz Urbanik Center for Probability and Mathematical Statistics
Language
English
Publisher DOI
Description
A stochastically continuous process ɛ(t), t ≥ 0, is said to be time-stable if the sum of n i.i.d. copies of ɛ equals in distribution the time-scaled stochastic process ɛ(nt), t ≥ 0. The paper advances the understanding of time-stable processes by means of their LePage series representations as the sum of i.i.d. processes with the arguments scaled by the sequence of successive points of the unit intensity Poisson process on [0, ∞). These series yield numerous examples of stochastic processes that share one-dimensional distributions with a Lévy process.