Details

Subject(s)

• Stochastic differential equations—Numerical solutions [Browse]

Author

• Kloeden, Peter E. [Browse]

Publisher

• Society for Industrial and Applied Mathematics [Browse]

Series

• Other titles in applied mathematics. [More in this series]
• [Other titles in applied mathematics] ; OT169

Restrictions note

Restricted to subscribers or individual electronic text purchasers.

Summary note

This book provides a lively and accessible introduction to the numerical solution of stochastic differential equations with the aim of making this subject available to the widest possible readership. Although introductory, the book covers a range of modern research topics, including Itô versus Stratonovich calculus, implicit methods, stability theory, nonconvergence on nonlinear problems, multilevel Monte Carlo, approximation of double stochastic integrals, and tau leaping for chemical and biochemical reaction networks. An Introduction to the Numerical Simulation of Stochastic Differential Equations presents an outline of the underlying convergence and stability theory while avoiding technical details, illustrates key ideas with numerous computational examples, lists computer code at the end of each chapter, and includes 150 exercises, with solutions available online, and 40 programming tasks. This textbook is appropriate for undergraduates and postgraduates in mathematics, engineering, physics, chemistry, finance, and related disciplines, as well as researchers in these areas. The material assumes only a competence in algebra and calculus at the level reached by a typical first-year undergraduate mathematics class, and prerequisites are kept to a minimum. Some familiarity with basic concepts from numerical analysis and probability is also desirable but not necessary.

Notes

Includes index.

Bibliographic references

Includes bibliographical references (pages 259-271) and index.

System details

• Mode of access: World Wide Web.
• System requirements: Adobe Acrobat Reader.

Source of description

Description based on title page of print version.

Contents

• Random variables
• Computer simulation
• Brownian motion
• Stochastic integrals
• Stochastic differential equations
• The Itô formula
• Itô versus Stratonovich
• Euler-Maruyama
• Weak convergence
• Strong convergence
• Implicit methods and numerical stability
• Mean exit times
• Exotic options
• Steady states
• Multilevel Monte Carlo
• Jumps
• Higher-order methods
• Systems of stochastic differential equations
• Numerical methods for systems
• Chemical kinetics.

Show 17 more Contents items

Other format(s)

Also available in print version.

ISBN

1-61197-643-X

Publisher no.

OT169

LCCN

2020042062

Doi

• 10.1137/1.9781611976434

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