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Selfdecomposable Fields

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

arXiv.org, 2015.

Research output: Working paper/Preprint Working paperResearch

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Barndorff-Nielsen, Ole E., Orimar Sauri and Benedykt Szozda Selfdecomposable Fields. arXiv.org. 2015., 33 p.

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Barndorff-Nielsen OE, Sauri O, Szozda B. Selfdecomposable Fields. arXiv.org. 2015 Feb 5.

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@techreport{547501f415294373b7fc65da9860ffb8,
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\'evy measure and the associated L\'evy-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 functions) for a Volterra field driven by a L\'evy 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\'evy processes, give the L\'evy-It\^o representation associated with them and study stochastic integration with respect to such processes. We provide examples in the form of L\'evy semistationary processes with a Gamma kernel and Ornstein-Uhlenbeck processes.",
keywords = "math.PR, 60E07, 60G51, 60G60",
author = "Barndorff-Nielsen, {Ole E.} and Orimar Sauri and Benedykt Szozda",
year = "2015",
month = feb,
day = "5",
language = "English",
publisher = "arXiv.org",
type = "WorkingPaper",
institution = "arXiv.org",

}

RIS

TY - UNPB

T1 - Selfdecomposable Fields

AU - Barndorff-Nielsen, Ole E.

AU - Sauri, Orimar

AU - Szozda, Benedykt

PY - 2015/2/5

Y1 - 2015/2/5

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 L\'evy measure and the associated L\'evy-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 functions) for a Volterra field driven by a L\'evy 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\'evy processes, give the L\'evy-It\^o representation associated with them and study stochastic integration with respect to such processes. We provide examples in the form of L\'evy 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 L\'evy measure and the associated L\'evy-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 functions) for a Volterra field driven by a L\'evy 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\'evy processes, give the L\'evy-It\^o representation associated with them and study stochastic integration with respect to such processes. We provide examples in the form of L\'evy semistationary processes with a Gamma kernel and Ornstein-Uhlenbeck processes.

KW - math.PR

KW - 60E07, 60G51, 60G60

M3 - Working paper

BT - Selfdecomposable Fields

PB - arXiv.org

ER -