Numerical Solution of Stochastic Differential Equations (Stochastic Modelling and Applied Probability, 23, Band 23) - Hardcover

Kloeden, Peter E.; Platen, Eckhard

Hardcover

ISBN 10: 3540540628 ISBN 13: 9783540540625

Verlag: Springer, 1999

Inhaltsangabe

The aim of this book is to provide an accessible introduction to stochastic differ­ ential equations and their applications together with a systematic presentation of methods available for their numerical solution. During the past decade there has been an accelerating interest in the de­ velopment of numerical methods for stochastic differential equations (SDEs). This activity has been as strong in the engineering and physical sciences as it has in mathematics, resulting inevitably in some duplication of effort due to an unfamiliarity with the developments in other disciplines. Much of the reported work has been motivated by the need to solve particular types of problems, for which, even more so than in the deterministic context, specific methods are required. The treatment has often been heuristic and ad hoc in character. Nevertheless, there are underlying principles present in many of the papers, an understanding of which will enable one to develop or apply appropriate numerical schemes for particular problems or classes of problems.

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Über die Autorin bzw. den Autor

Peter E. Kloeden is retired Chair of Applied and Instrumental Mathematics is the Goethe University Frankfurt and is now a visiting researcher at the University of Tübingen. His research interests include analysis and numerics of random and nonautonomous systems and their applications. He is a Fellow of SIAM and was awarded the W. T. and Idalia Reid Prizefrom SIAM in 2006. In 2014, he received a Thousand Talents Award from the government of China. He served as co-editor-in-chief of Discrete and Continuous Dynamical Systems, Series B. He is the co-author of best selling books on stochastic numerics, numerical dynamics, nonautonomous dynamical systems, lattice systems, fuzzy metric spaces, etc.

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The numerical analysis of stochastic differential equations differs significantly from that of ordinary differential equations due to peculiarities of stochastic calculus. This book provides an introduction to stochastic calculus and stochastic differential equations, in both theory and applications, emphasising 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. The book is also accessible to others who only require numerical recipes. The stochastic Taylor expansion provides the basis for the discrete time numerical methods for differential equations. The book presents many new results on high-order methods for strong sample path approximations and for weak functional approximations, including implicit, predictor-corrector, extra-polation 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 research problems in a field that is just beginning to expand rapidly and is widely applicable. 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.

Details zur Ausgabe

• Verlag: Springer
• Erscheinungsdatum: 1999
• Sprache: Englisch
• ISBN 10: 3540540628
• ISBN 13: 9783540540625
• Einband: Gebundene Ausgabe
• Anzahl der Seiten: 672
• Kontakt zum Hersteller: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3; Heidelberg; 69115; Deutschland