Lévy Processes and Stochastic Calculus
Seiten
2009
|
2nd Revised edition
Cambridge University Press (Verlag)
9780521738651 (ISBN)
Cambridge University Press (Verlag)
9780521738651 (ISBN)
A unique development of these two subjects contained in a single volume. New topics featured in this fully revised edition include regular variation and subexponential distributions, characterisation of Lévy processes with finite variation, multiple Wiener-Lévy integrals and chaos decomposition, and introductions to Malliavin calculus and stability theory for Lévy-driven SDEs.
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.
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.
David Applebaum is a Professor in the Department of Probability and Statistics at the University of Sheffield.
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.
| Erscheint lt. Verlag | 30.4.2009 |
|---|---|
| Reihe/Serie | Cambridge Studies in Advanced Mathematics |
| Zusatzinfo | Worked examples or Exercises |
| Verlagsort | Cambridge |
| Sprache | englisch |
| Maße | 150 x 226 mm |
| Gewicht | 730 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik | |
| ISBN-13 | 9780521738651 / 9780521738651 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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