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Lévy Processes and Stochastic Calculus
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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; characterisation 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.
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Cambridge University Press; April 2009
492 pages; ISBN 9780511530784
Read online, or download in secure PDF format
492 pages; ISBN 9780511530784
Read online, or download in secure PDF format
Subject categories
- Academic > Mathematics > Probabilities. Mathematical statistics > Stochastic processes
- Academic > Mathematics > Probabilities. Mathematical statistics > Markov processes
- Academic > Mathematics > Probabilities. Mathematical statistics > Random walks (Mathematics)
- Academic > Mathematics > General
- Mathematics > Calculus
ISBNs
0511530781
9780511530784
9780521738651