Lvy Processes and Stochastic Calculus

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
characterization 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."