Bücher der Reihe Levy Matters

This three-chapter volume concerns the distributions of certain functionals of Levy processes. The first chapter, by Makoto Maejima, surveys representations of the main sub-classes of infinitesimal distributions in terms of mappings of certain Levy processes via stochastic integration.

The aim of this volume is to provide an extensive account of the most recent advances in statistics for discretely observed Levy processes. The chapters cover the main aspects of the estimation of discretely observed Levy processes, when the observation scheme is regular, from an up-to-date viewpoint.

Presenting some recent results on the construction and the moments of Levy-type processes, the focus of this volume is on a new existence theorem, which is proved using a parametrix construction. Levy-type processes behave locally like Levy processes but, in contrast to Levy processes, they are not homogeneous in space.

This volume presents recent developments in the area of Levy-type processes and more general stochastic processes that behave locally like a Levy process.