Lévy Processes and Stochastic Calculus (Cambridge Studies in

Lévy Processes and Stochastic Calculus (Cambridge Studies in Advanced Mathematics)

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

Lévy Processes and Stochastic Calculus (Cambridge Studies in Advanced Mathematics)