Lvy Processes and Stochastic Calculus

Lvy 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 Lvy processes, then leading on to develop the stochastic calculus for Lvy 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 Lvy processes to have finite moments; characterisation of Lvy processes with finite variation; Kunita's estimates for moments of Lvy type stochastic integrals; new proofs of Ito representation and martingale representation theorems for general Lvy processes; multiple Wiener-Lvy integrals and chaos decomposition; an introduction to Malliavin calculus; an introduction to stability theory for Lvy-driven SDEs.