Levy 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 Levy processes, then leading on to develop the stochastic calculus for Levy 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 Levy processes to have finite moments; characterisation of Levy processes with finite variation; Kunita's estimates for moments of Levy type stochastic integrals; new proofs of Ito representation and martingale representation theorems for general Levy processes; multiple Wiener-Levy integrals and chaos decomposition; an introduction to Malliavin calculus; an introduction to stability theory for Levy-driven SDEs.
Publisher: Cambridge University Press
Number of pages: 492
Weight: 730 g
Dimensions: 228 x 152 x 25 mm
Edition: 2nd Revised edition
'The book introduces all the tools that are needed for the stochastic approach to option pricing, including Ito's formula, Girsanov's theorem and the martingale representation theorem.' L'Enseignement Mathematique
'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 Levy processes accessible to a broad mathematical audience.' Mathematical Reviews