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Probability Measures, Lévy Measures, and Analyticity in Time

Research output: Working paper/Preprint Working paperResearch


  • Department of Mathematical Sciences
  • T.N. Thiele Centre
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 byproduct we investigate the smoothness of the semigroup density in time. Several concrete examples illustrate the three methods and our results.
Original languageEnglish
PublisherThiele Centre, Institut for Matematiske Fag, Aarhus Universitet
Number of pages43
Publication statusPublished - 12 Jul 2006

Bibliographical note

Published in Bernoulli 14, 764-790.

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