Bernoulli

  • Bernoulli
  • Volume 14, Number 3 (2008), 764-790.

Probability measures, Lévy measures and analyticity in time

Ole E. Barndorff-Nielsen and Friedrich Hubalek

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Abstract

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.

Article information

Source
Bernoulli Volume 14, Number 3 (2008), 764-790.

Dates
First available in Project Euclid: 25 August 2008

Permanent link to this document
https://projecteuclid.org/euclid.bj/1219669629

Digital Object Identifier
doi:10.3150/07-BEJ6114

Mathematical Reviews number (MathSciNet)
MR2537811

Zentralblatt MATH identifier
1162.60013

Keywords
cancellation of singularities exponential formula generalised gamma convolutions subordinators

Citation

Barndorff-Nielsen, Ole E.; Hubalek, Friedrich. Probability measures, Lévy measures and analyticity in time. Bernoulli 14 (2008), no. 3, 764--790. doi:10.3150/07-BEJ6114. https://projecteuclid.org/euclid.bj/1219669629


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