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Numerische Analysis stochastischer Differentialgleichungen unterscheidet sich deutlich von gewöhnlichen Differentialgleichungen durch die Besonderheiten stochastischen Rechnens. Das vorliegende Buch bietet Lesern mit "undergraduate" Kenntnissen eine leicht zugängliche Einführung in Stochastischen Differentialgleichungen, Anwendungen und Numerische Methoden für Physik und Technik. Zahlreiche Übungen sollen intuitives Verstehen und numerisches Geschick des Lesers fördern. Es wendet sich an Ingenieure, Physiker und Mathematiker die numerische Schemata für Anwendungen von Stochastischen Differentialgleichungen entwickeln und an Wissenschaftler aus anderen Gebieten, wie Biologie, Chemie oder Wirtschaftswissenschaften, mit weniger mathematischen Kenntnissen, die bestehende numerische Methoden für ihre eigene Arbeit verwenden wollen.
Inhaltsverzeichnis
1. Probability and Statistics.- 2. Probability and Stochastic Processes.- 3. Ito Stochastic Calculus.- 4. Stochastic Differential Equations.- 5. Stochastic Taylor Expansions.- 6. Modelling with Stochastic Differential Equations.- 7. Applications of Stochastic Differential Equations.- 8. Time Discrete Approximation of Deterministic Differential Equations.- 9. Introduction to Stochastic Time Discrete Approximation.- 10. Strong Taylor Approximations.- 11. Explicit Strong Approximations.- 12. Implicit Strong Approximations.- 13. Selected Applications of Strong Approximations.- 14. Weak Taylor Approximations.- 15. Explicit and Implicit Weak Approximations.- 16. Variance Reduction Methods.- 17. Selected Applications of Weak Approximations.- Solutions of Exercises.- Bibliographical Notes.
Über den Autor / die Autorin
Professor Eckhard Platen is a joint appointment between the School of Finance and Economics and the Department of Mathematical Sciences to the 1997 created Chair in Quantitative Finance at the University of Technology Sydney. Prior to this appointment he was Founding Head of the Centre for Financial Mathematics at the Institute of Advanced Studies at the Australian National University in Canberra. He completed a PhD in Mathematics at the Technical University in Dresden in 1975 and obtained in 1985 his Dr. sc. from the Academy of Sciences in Berlin, where he headed at the Weierstrass Institute the Sector of Stochastics. He is co-author of two successful books on Numerical Methods for Stochastic Differential Equations, published by Springer Verlag, and has authored more than 100 research papers in quantitative finance and mathematics.
Bericht
"... the authors draw upon their own research and experiences in obviously many disciplines... considerable time has obviously been spent writing this in the simplest language possible. This was not an easy task... Their exposition stresses clarity, not formality - a very welcome approach." ZAMP
