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

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David Applebaum
Cambridge University Press
Edition: 2, 4/30/2009
EAN 9780521738651, ISBN10: 0521738652

Paperback, 492 pages, 22.9 x 15.2 x 3.1 cm
Language: English

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

Preface to second edition
Preface to first edition
Overview
Notation
1. LÃƒÂ©vy processes
2. Martingales, stopping times and random measures
3. Markov processes, semigroups and generators
4. Stochastic integration
5. Exponential martingales
6. Stochastic differential equations
References
Index of notation
Subject index.