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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 ItoÌ 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 ItoÌ formula
ItoÌ 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.
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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