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Lévy Processes and Stochastic Calculus

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Lévy Processes and Stochastic Calculus by David Applebaum, 9780521738651
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  • ISBN: 9780521738651 | 0521738652
  • Cover: Paperback
  • Copyright: 5/11/2009
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L_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 L_vy processes, then leading on to develop the stochastic calculus for L_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 L_vy processes to have finite moments; characterization of L_vy processes with finite variation; Kunita's estimates for moments of L_vy type stochastic integrals; new proofs of Ito representation and martingale representation theorems for general L_vy processes; multiple Wiener-L_vy integrals and chaos decomposition; an introduction to Malliavin calculus; an introduction to stability theory for L_vy-driven SDEs.

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