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