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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; characterization 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.Read more
- 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
Reviews & endorsements
"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 stochastic calculus. The 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."
Dora Selesi, Mathematical Reviews
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- Edition: 2nd Edition
- Date Published: May 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
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
Index of notation
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