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＜電子ブック＞
Numerical Solution of Stochastic Differential Equations / by Peter E. Kloeden, Eckhard Platen
(Stochastic Modelling and Applied Probability. ISSN:2197439X ; 23)

版	1st ed. 1992.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	1992
本文言語	英語
大きさ	XXXVI, 636 p : online resource
著者標目	*Kloeden, Peter E author Platen, Eckhard author SpringerLink (Online service)
件　名	LCSH:Probabilities LCSH:Mathematical analysis LCSH:Numerical analysis LCSH:Statistics  LCSH:Mathematical physics LCSH:Engineering mathematics LCSH:Engineering -- Data processing  全ての件名で検索 FREE:Probability Theory FREE:Analysis FREE:Numerical Analysis FREE:Statistics in Business, Management, Economics, Finance, Insurance FREE:Theoretical, Mathematical and Computational Physics FREE:Mathematical and Computational Engineering Applications
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-3-662-12616-5

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