The aim of this volume is to provide an extensive account of the most recent advances in
statistics for discretely observed Lévy processes. These days statistics for stochastic
processes is a lively topic driven by the needs of various fields of application such as
finance the biosciences and telecommunication. The three chapters of this volume are
completely dedicated to the estimation of Lévy processes and are written by experts in the
field. The first chapter by Denis Belomestny and Markus Reiß treats the low frequency situation
and estimation methods are based on the empirical characteristic function. The second chapter
by Fabienne Comte and Valery Genon-Catalon is dedicated to non-parametric estimation mainly
covering the high-frequency data case. A distinctive feature of this part is the construction
of adaptive estimators based on deconvolution or projection or kernel methods. The last
chapter by Hiroki Masuda considers the parametric situation. The chapters cover the main
aspects of the estimation of discretely observed Lévy processes when the observation scheme is
regular from an up-to-date viewpoint.
