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Cover: 9783540540625 | Numerical Solution of Stochastic Differential Equations | Buch | XXXVI
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Numerical Solution of Stochastic Differential Equations
Buch von Eckhard Platen (u. a.)
Sprache: Englisch

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Beschreibung
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.
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.
Zusammenfassung
The numerical analysis of stochastic differential equations (SDEs) differs significantly from that of ordinary differential equations, due to the peculiarities of stochastic calculus. This book provides an easily accessible introduction to SDEs, their applications and the numerical methods to solve such equations. To help the reader develop an intuitive understanding and hands-on numerical skills, numerous exercises and PC-Exercises are included. The book is directed at a multi-disciplinary readership, consisting primarily of engineers, financial analysts, physicists and mathematicians developing numerical schemes for applications of SDEs, and also of researchers in other fields like biology, chemistry or economics who, with less mathematical background, wish to apply
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.
Details
Erscheinungsjahr: 1992
Fachbereich: Analysis
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Reihe: Stochastic Modelling and Applied Probability
Inhalt: xxxvi
636 S.
ISBN-13: 9783540540625
ISBN-10: 3540540628
Sprache: Englisch
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Platen, Eckhard
Kloeden, Peter E.
Hersteller: Springer-Verlag GmbH
Springer Berlin Heidelberg
Stochastic Modelling and Applied Probability
Maße: 241 x 160 x 42 mm
Von/Mit: Eckhard Platen (u. a.)
Erscheinungsdatum: 06.08.1992
Gewicht: 1,168 kg
Artikel-ID: 102342625
Zusammenfassung
The numerical analysis of stochastic differential equations (SDEs) differs significantly from that of ordinary differential equations, due to the peculiarities of stochastic calculus. This book provides an easily accessible introduction to SDEs, their applications and the numerical methods to solve such equations. To help the reader develop an intuitive understanding and hands-on numerical skills, numerous exercises and PC-Exercises are included. The book is directed at a multi-disciplinary readership, consisting primarily of engineers, financial analysts, physicists and mathematicians developing numerical schemes for applications of SDEs, and also of researchers in other fields like biology, chemistry or economics who, with less mathematical background, wish to apply
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.
Details
Erscheinungsjahr: 1992
Fachbereich: Analysis
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Reihe: Stochastic Modelling and Applied Probability
Inhalt: xxxvi
636 S.
ISBN-13: 9783540540625
ISBN-10: 3540540628
Sprache: Englisch
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Platen, Eckhard
Kloeden, Peter E.
Hersteller: Springer-Verlag GmbH
Springer Berlin Heidelberg
Stochastic Modelling and Applied Probability
Maße: 241 x 160 x 42 mm
Von/Mit: Eckhard Platen (u. a.)
Erscheinungsdatum: 06.08.1992
Gewicht: 1,168 kg
Artikel-ID: 102342625
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