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 language
English
Publisher
Thiele Centre, Institut for Matematiske Fag, Aarhus Universitet
