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Levy processes and stochastic calculus

✍ Scribed by David Applebaum

Publisher
Cambridge University Press
Year
2009
Tongue
English
Leaves
492
Series
Cambridge Studies in Advanced Mathematics 116
Edition
2
Category
Library
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✦ Synopsis

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

✦ Subjects

Математика;Теория вероятностей и математическая статистика;Теория случайных процессов;

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