Selfdecomposable Fields

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

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

2 Citationer (Scopus)

Resumé

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.
OriginalsprogEngelsk
TidsskriftJournal of Theoretical Probability
Vol/bind30
Udgave nummer1
Sider (fra-til)233-267
Antal sider35
ISSN0894-9840
DOI
StatusUdgivet - 2017

Fingerprint

Self-decomposability
Volterra
Random Field
Stochastic Integration
Infinitely Divisible
Valued Fields
Kernel Function
Dilation
kernel
Necessary Conditions
Sufficient Conditions

Citer dette

Barndorff-Nielsen, Ole E ; Orimar, Sauri Arregui ; Szozda, Benedykt. / Selfdecomposable Fields. I: Journal of Theoretical Probability. 2017 ; Bind 30, Nr. 1. s. 233-267.
@article{479baab4eab84b9b8a054eb1a7d18f25,
title = "Selfdecomposable Fields",
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 L{\'e}vy measure and the associated L{\'e}vy-It{\^o} 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 L{\'e}vy 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 L{\'e}vy processes, give the L{\'e}vy-It{\^o} representation associated with them and study stochastic integration with respect to such processes. We provide examples in the form of L{\'e}vy semistationary processes with a Gamma kernel and Ornstein–Uhlenbeck processes.",
author = "Barndorff-Nielsen, {Ole E} and Orimar, {Sauri Arregui} and Benedykt Szozda",
year = "2017",
doi = "10.1007/s10959-015-0630-z",
language = "English",
volume = "30",
pages = "233--267",
journal = "Journal of Theoretical Probability",
issn = "0894-9840",
publisher = "Springer",
number = "1",

}

Barndorff-Nielsen, OE, Orimar, SA & Szozda, B 2017, 'Selfdecomposable Fields', Journal of Theoretical Probability, bind 30, nr. 1, s. 233-267. https://doi.org/10.1007/s10959-015-0630-z

Selfdecomposable Fields. / Barndorff-Nielsen, Ole E; Orimar, Sauri Arregui; Szozda, Benedykt.

I: Journal of Theoretical Probability, Bind 30, Nr. 1, 2017, s. 233-267.

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

TY - JOUR

T1 - Selfdecomposable Fields

AU - Barndorff-Nielsen, Ole E

AU - Orimar, Sauri Arregui

AU - Szozda, Benedykt

PY - 2017

Y1 - 2017

N2 - 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.

AB - 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.

U2 - 10.1007/s10959-015-0630-z

DO - 10.1007/s10959-015-0630-z

M3 - Journal article

VL - 30

SP - 233

EP - 267

JO - Journal of Theoretical Probability

JF - Journal of Theoretical Probability

SN - 0894-9840

IS - 1

ER -