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Lévy Matters VI

Lévy-Type Processes: Moments, Construction and Heat Kernel Estimates

  • Franziska Kühn

Part of the Lecture Notes in Mathematics book series (LNM, volume 2187)

Also part of the Lévy Matters book sub series (LEVY, volume 2187)

Table of contents

  1. Front Matter
    Pages i-xxiii
  2. Franziska Kühn
    Pages 1-29
  3. Franziska Kühn
    Pages 31-50
  4. Franziska Kühn
    Pages 51-65
  5. Franziska Kühn
    Pages 67-165
  6. Franziska Kühn
    Pages 167-214
  7. Back Matter
    Pages 215-245

About this book

Introduction

Presenting some recent results on the construction and the moments of Lévy-type processes, the focus of this volume is on a new existence theorem, which is proved using a parametrix construction. Applications range from heat kernel estimates for a class of Lévy-type processes to existence and uniqueness theorems for Lévy-driven stochastic differential equations with Hölder continuous coefficients. Moreover, necessary and sufficient conditions for the existence of moments of Lévy-type processes are studied and some estimates on moments are derived. Lévy-type processes behave locally like Lévy processes but, in contrast to Lévy processes, they are not homogeneous in space. Typical examples are processes with varying index of stability and solutions of Lévy-driven stochastic differential equations.

This is the sixth volume in a subseries of the Lecture Notes in Mathematics called Lévy Matters. Each volume describes a number of important topics in the theory or applicati
ons of Lévy processes and pays tribute to the state of the art of this rapidly evolving subject, with special emphasis on the non-Brownian world.

Keywords

Feller processes Lévy-type processes parametrix construction existence result heat kernel estimates stable-like processes variable order subordination moment estimates Lévy-driven stochastic differential equations symbols of varying order

Authors and affiliations

  • Franziska Kühn
    • 1
  1. 1.Institut für Mathematische StochastikTechnische Universität DresdenDresdenGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-60888-4
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-60887-7
  • Online ISBN 978-3-319-60888-4
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site
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