Product Description

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

• Amazon Sales Rank: #1007979 in Books
• Published on: 2009-05-11
• Original language: English
• Number of items: 1
• Binding: Paperback
• 490 pages

Review
"I would recommend this book as a reference textbook for advanced courses like stochastic modeling or stochastic calculus in finance."
Alexander Novikov, University of Technology

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

Customer Reviews

ok book
but there are better books out there on stochastic calculus
and Levy processes. The material covered is essentially a rewriting of existing mathematics. There are also minor math mistakes throughout. For example on page 197, the definition
of stochastic integration and the definition of random
measures on page 89 are consistent for defining stochastic
integration with respect to Brownian motion only if we
we assume Brownian motion is a function of finite variation which is not.