Lévy Processes and Stochastic Calculus (Cambridge Studies in Advanced Mathematics, Series Number 116) - Softcover

Applebaum, David

Softcover

ISBN 10: 0521738652 ISBN 13: 9780521738651

Publisher: Cambridge University Press, 2009

Synopsis

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.

About this title

About the Author

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

Edition details

• Publisher: Cambridge University Press
• Publication date: 2009
• Language: English
• ISBN 10: 0521738652
• ISBN 13: 9780521738651
• Binding: Paperback
• Edition number: 2
• Number of pages: 492