© 2015

Lévy Matters IV

Estimation for Discretely Observed Lévy Processes


Part of the Lecture Notes in Mathematics book series (LNM, volume 2128)

Also part of the Lévy Matters book sub series (LEVY, volume 2128)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Denis Belomestny, Markus Reiß
    Pages 1-76
  3. Fabienne Comte, Valentine Genon-Catalot
    Pages 77-177
  4. Hiroki Masuda
    Pages 179-286
  5. Back Matter
    Pages 287-288

About this book


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.


60G10,60G70,60J10,62G05,62M05,60F05,62F12,91B28 Adaptive estimation Estimation with discrete observations Non-parametric estimation Parametric estimation of Lévy processes Spectral estimators

Authors and affiliations

  1. 1.Duisburg-Essen University, Faculty of Mathematics, Thea-Leymann-Str. 9, D-45127 Essen, Germany and National University Higher School of EconomicsMoscowRussia
  2. 2.MAP5, UMR CNRS 8145University Paris Descartes, Sorbonne Paris CitéParisFrance
  3. 3.MAP5, UMR CNRS 8145University Paris Descartes, Sorbonne Paris CitéParisFrance
  4. 4.Institute of Mathematics for IndustryKyushu UniversityFukuokaJapan
  5. 5.Institut für MathematikHumboldt-Universität zu BerlinBerlinGermany

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“This is a remarkable collection presenting different but important aspects in statistical inference problems for Lévy processes based on discrete observations. The authors of the three chapters have made essential contributions in this area. All three chapters are carefully written and referenced. PhD students and professionals in stochastic modelling will benefit a lot from this volume.” (Jordan M. Stoyanov, zbMATH 1330.60002, 2016)