Levy Processes and Stochastic Calculus
(Sprache: Englisch)
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,...
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Klappentext zu „Levy Processes and Stochastic Calculus “
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.
Inhaltsverzeichnis zu „Levy Processes and Stochastic Calculus “
Preface to second edition; Preface to first edition; Overview; Notation; 1. Lévy 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.
Autoren-Porträt von David Applebaum
David Appelbaum has previously worked at a University as well as in publishing. His most recent books include notes on water: an aqueous phenomenology [Monkfish, 2018].
Bibliographische Angaben
- Autor: David Applebaum
- 492 Seiten, Maße: 15,2 x 22,9 cm, Kartoniert (TB), Englisch
- Verlag: Cambridge University Press
- ISBN-10: 0521738652
- ISBN-13: 9780521738651
- Erscheinungsdatum: 12.05.2014
Sprache:
Englisch
Rezension zu „Levy Processes and Stochastic Calculus “
'The book introduces all the tools that are needed for the stochastic approach to option pricing, including Ito's formula, Girsanov's theorem and the martingale representation theorem.' L'Enseignement Mathematique 'The monograph provides a good introduction to the subject, the exposition is clear and systematic, the key points and proofs are easy to follow; therefore it can be a valuable guide both as a textbook for graduate students and as a reference for researchers in the field of stochiastic calculus ... This book is written with great care and precision. Due to its lucid and comprehensive style of presentation, it will make the theory of Levy processes accessible to a broad mathematical audience.' Mathematical Reviews
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