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Lévy Matters VI

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

  • Book
  • © 2017

Overview

Authors:
  1. Franziska Kühn

    1. Institut für Mathematische Stochastik, Technische Universität Dresden, Dresden, Germany

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  • All results are illustrated with numerous applications
  • Numerous examples of Lévy-type processes offer new possibilities to model irregular phenomena
  • Detailed explanations help the reader to get a better understanding of Lévy-type processes

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

Part of the book sub series: Lévy Matters (LEVY)

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-xxiii
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  2. Basics

    • Franziska Kühn
    Pages 1-29

  3. Moments of Lévy-Type Processes

    • Franziska Kühn
    Pages 31-50

  4. Parametrix Construction

    • Franziska Kühn
    Pages 51-65

  5. Parametrix Construction: Proofs

    • Franziska Kühn
    Pages 67-165

  6. Applications

    • Franziska Kühn
    Pages 167-214

  7. Back Matter

    Pages 215-245
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Keywords

About this book

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 applicationsof Lévy processes and pays tribute to the state of the art of this rapidly evolving subject, with special emphasis on the non-Brownian world.

Authors and Affiliations

  • Institut für Mathematische Stochastik, Technische Universität Dresden, Dresden, Germany

    Franziska Kühn

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