NDLI: Selfdecomposable Fields

Content Provider	Springer Nature Link
Author	Barndorff Nielsen, Ole E. Sauri, Orimar Szozda, Benedykt
Copyright Year	2015
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.
Ending Page	267
Page Count	35
Starting Page	233
File Format	PDF
ISSN	08949840
e-ISSN	15729230
Journal	Journal of Theoretical Probability
Issue Number	1
Volume Number	30
Language	English
Publisher	Springer US
Publisher Date	2015-07-29
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Selfdecomposability of random fields Urbanik classes of random fields Volterra fields Random fields Probability Theory and Stochastic Processes Infinitely divisible distributions; stable distributions Statistics Processes with independent increments; LÃ©vy processes
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Statistics, Probability and Uncertainty

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