Lévy processes form a wide and rich class of random process, and have many applications ranging from physics to finance. Stochastic calculus is the mathematics of systems interacting with random noise. Here, the author ties these two subjects together, beginning with an introduction to the general theory of Lévy processes, then leading on to develop the stochastic calculus for Lévy processes in a direct and accessible way. This fully revised edition now features a number of new topics. These include: regular variation and subexponential distributions; necessary and sufficient conditions for Lévy processes to have finite moments; characterisation of Lévy processes with finite variation; Kunita's estimates for moments of Lévy type stochastic integrals; new proofs of Ito representation and martingale representation theorems for general Lévy processes; multiple Wiener-Lévy integrals and chaos decomposition; an introduction to Malliavin calculus; an introduction to stability theory for Lévy-driven SDEs.
- Now fully revised by the author and featuring new topics such as regular variation and subexponential distributions
- A unique development of stochastic integrals and stochastic differential equations driven by Lévy processes
- Discusses all the tools needed for a stochastic approach to option pricing
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Reviews & endorsements
'The book introduces all the tools that are needed for the stochastic approach to option pricing, including Itô's formula, Girsanov's theorem and the martingale representation theorem.' L'Enseignement Mathématique
'The monograph provides a good introduction to the subject, the exposition is clear and systematic, the key points and proofs are easy to follow; therefore it can be a valuable guide both as a textbook for graduate students and as a reference for researchers in the field of stochiastic calculus … This book is written with great care and precision. Due to its lucid and comprehensive style of presentation, it will make the theory of Lévy processes accessible to a broad mathematical audience.' Mathematical Reviews
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Product details
- Edition: 2nd Edition
- Date Published: April 2009
- format: Paperback
- isbn: 9780521738651
- length: 492 pages
- dimensions: 226 x 150 x 25 mm
- weight: 0.73kg
- contains: 130 exercises
- availability: Available
Table of Contents
Preface to second edition
Preface to first edition
Overview
Notation
1. Lévy processes
2. Martingales, stopping times and random measures
3. Markov processes, semigroups and generators
4. Stochastic integration
5. Exponential martingales
6. Stochastic differential equations
References
Index of notation
Subject index.
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Lévy Processes and Stochastic Calculus

David Applebaum
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- Errata
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Author
David Applebaum, University of Sheffield
David Applebaum is a Professor in the Department of Probability and Statistics at the University of Sheffield.