Selfdecomposable Fields

Ole E Barndorff-Nielsen, Sauri Arregui Orimar, Benedykt Szozda

Research output: Contribution to journalJournal articleResearchpeer-review

3 Citations (Scopus)


In the present paper, we study selfdecomposability of random fields, as defined directly rather than in terms of finite-dimensional distributions. The main tools in our analysis are the master Lévy measure and the associated Lévy-Itô representation. We give the dilation criterion for selfdecomposability analogous to the classical one. Next, we give necessary and sufficient conditions (in terms of the kernel function) for a Volterra field driven by a Lévy basis to be selfdecomposable. In this context, we also study the so-called Urbanik classes of random fields. We follow this with the study of existence and selfdecomposability of integrated Volterra fields. Finally, we introduce infinitely divisible field-valued Lévy processes, give the Lévy-Itô representation associated with them and study stochastic integration with respect to such processes. We provide examples in the form of Lévy semistationary processes with a Gamma kernel and Ornstein–Uhlenbeck processes.
Original languageEnglish
JournalJournal of Theoretical Probability
Issue number1
Pages (from-to)233-267
Number of pages35
Publication statusPublished - 2017


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