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Probability measures, Lévy measures and analyticity in time

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Probability measures, Lévy measures and analyticity in time. / Barndorff-Nielsen, Ole Eiler; Hubalek, Friedrich.

I: Bernoulli, Bind 14, Nr. 3, 2008, s. 764-790.

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avisTidsskriftartikelForskningpeer review

Harvard

Barndorff-Nielsen, OE & Hubalek, F 2008, 'Probability measures, Lévy measures and analyticity in time', Bernoulli, bind 14, nr. 3, s. 764-790. https://doi.org/10.3150/07-BEJ6114

APA

Barndorff-Nielsen, O. E., & Hubalek, F. (2008). Probability measures, Lévy measures and analyticity in time. Bernoulli, 14(3), 764-790. https://doi.org/10.3150/07-BEJ6114

CBE

Barndorff-Nielsen OE, Hubalek F. 2008. Probability measures, Lévy measures and analyticity in time. Bernoulli. 14(3):764-790. https://doi.org/10.3150/07-BEJ6114

MLA

Barndorff-Nielsen, Ole Eiler og Friedrich Hubalek. "Probability measures, Lévy measures and analyticity in time". Bernoulli. 2008, 14(3). 764-790. https://doi.org/10.3150/07-BEJ6114

Vancouver

Barndorff-Nielsen OE, Hubalek F. Probability measures, Lévy measures and analyticity in time. Bernoulli. 2008;14(3):764-790. https://doi.org/10.3150/07-BEJ6114

Author

Barndorff-Nielsen, Ole Eiler ; Hubalek, Friedrich. / Probability measures, Lévy measures and analyticity in time. I: Bernoulli. 2008 ; Bind 14, Nr. 3. s. 764-790.

Bibtex

@article{edb04520e5f611dc9afb000ea68e967b,
title = "Probability measures, L{\'e}vy measures and analyticity in time",
abstract = "We investigate the relation of the semigroup probability density of an infinite activity L{\'e}vy process to the corresponding L{\'e}vy density. For subordinators, we provide three methods to compute the former from the latter. The first method is based on approximating compound Poisson distributions, the second method uses convolution integrals of the upper tail integral of the L{\'e}vy measure and the third method uses the analytic continuation of the L{\'e}vy density to a complex cone and contour integration. As a by-product, we investigate the smoothness of the semigroup density in time. Several concrete examples illustrate the three methods and our results.",
author = "Barndorff-Nielsen, {Ole Eiler} and Friedrich Hubalek",
year = "2008",
doi = "10.3150/07-BEJ6114",
language = "English",
volume = "14",
pages = "764--790",
journal = "Bernoulli",
issn = "1350-7265",
publisher = "International Statistical Institute",
number = "3",

}

RIS

TY - JOUR

T1 - Probability measures, Lévy measures and analyticity in time

AU - Barndorff-Nielsen, Ole Eiler

AU - Hubalek, Friedrich

PY - 2008

Y1 - 2008

N2 - We investigate the relation of the semigroup probability density of an infinite activity Lévy process to the corresponding Lévy density. For subordinators, we provide three methods to compute the former from the latter. The first method is based on approximating compound Poisson distributions, the second method uses convolution integrals of the upper tail integral of the Lévy measure and the third method uses the analytic continuation of the Lévy density to a complex cone and contour integration. As a by-product, we investigate the smoothness of the semigroup density in time. Several concrete examples illustrate the three methods and our results.

AB - We investigate the relation of the semigroup probability density of an infinite activity Lévy process to the corresponding Lévy density. For subordinators, we provide three methods to compute the former from the latter. The first method is based on approximating compound Poisson distributions, the second method uses convolution integrals of the upper tail integral of the Lévy measure and the third method uses the analytic continuation of the Lévy density to a complex cone and contour integration. As a by-product, we investigate the smoothness of the semigroup density in time. Several concrete examples illustrate the three methods and our results.

U2 - 10.3150/07-BEJ6114

DO - 10.3150/07-BEJ6114

M3 - Journal article

VL - 14

SP - 764

EP - 790

JO - Bernoulli

JF - Bernoulli

SN - 1350-7265

IS - 3

ER -