Lévy Processes and Stochastic Calculus

A fully revised and appended edition of this unique volume, which develops together these two important subjects.

David Applebaum (Author)

9780521738651, Cambridge University Press

Paperback, published 30 April 2009

492 pages, 130 exercises
22.6 x 15 x 2.5 cm, 0.73 kg

'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

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.

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.

Subject Areas: Stochastics [PBWL], Differential calculus & equations [PBKJ]