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.
Originalsprog | Engelsk |
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Tidsskrift | Journal of Theoretical Probability |
Vol/bind | 30 |
Udgave nummer | 1 |
Sider (fra-til) | 233-267 |
Antal sider | 35 |
ISSN | 0894-9840 |
DOI | |
Status | Udgivet - 2017 |