Levy processes and stochastic calculus
By: Applebaum, David.
Series: Cambridge studies in advanced mathematics / edited by B. Bollobas; v.116. Publisher: Cambridge Cambridge University Press 2009Edition: 2nd ed.Description: xxx, 460p.ISBN: 9780521738651.Subject(s): Stochastic analysisDDC classification: 519.22 | Ap52l2 Summary: 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.| Item type | Current location | Collection | Call number | Status | Date due | Barcode | Item holds |
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Books
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PK Kelkar Library, IIT Kanpur | General Stacks | 519.22 Ap52l2 (Browse shelf) | Checked out to MANGALA PRASAD (S2110826600) | 20/05/2024 | A184022 |
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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