Numerical Solution of Stochastic Differential Equations

15Numerische 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.07The book presents many new results on higher-order methods for strong sample path approximations and for weak functional approximations, including implicit, predictor-corrector, extrapolation and variance-reduction methods. Besides serving as a basic text on such methods, the book offers the reader ready access to a large number of potential resarch problems in a field that is just beginning to expand rapidly and is widely applicable.16The numerical analysis of stochastic differential equations differs significantly from that of ordinary differential equations due to the peculiarities of stochastic calculus. This book provides an introduction to stochastic calculus and stochastic differential equations, in both theory and applications, emphasizing the numerical methods needed to solve such equations. It assumes of the reader an undergraduate background in mathematical methods typical of engineers and physicists, though many chapters begin with a descriptive summary, accessible to others who only require numerical recipes. To help the reader to develop an intuitive understanding of the underlying mathematics and hand-on numerical skills, exercises and over 100 PC-Exercises are included. The stochastic Taylor expansion provides discrete time numerical methods for stochastic differential equations.13"... 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." ZAMP02Professor 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.