Selfdecomposable Fields

Ole Barndorff-Nielsen, Orimar Sauri () and Benedykt Szozda ()
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Orimar Sauri: Aarhus University
Benedykt Szozda: Aarhus University

Journal of Theoretical Probability, 2017, vol. 30, issue 1, 233-267

Abstract: Abstract 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.

Keywords: Selfdecomposability of random fields; Urbanik classes of random fields; Random fields; Volterra fields; 60E07; 60G51; 60G60 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10959-015-0630-z

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