Lévy Processes and Stochastic Calculus

by David Applebaum

Overview

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.

Product Details

ISBN-13:	9780521738651
Publisher:	Cambridge University Press
Publication date:	04/30/2009
Series:	Cambridge Studies in Advanced Mathematics , #116
Edition description:	New Edition
Pages:	492
Product dimensions:	6.00(w) x 8.90(h) x 1.00(d)

About the Author

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

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.

Editorial Reviews

"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

From the Publisher