Synopsis
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. It presents an outline of the underlying convergence and stability theory while avoiding technical details. Key ideas are illustrated with numerous computational examples and computer code is listed at the end of each chapter. The authors include 150 exercises, with solutions available online, and 40 programming tasks. 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 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.
About the Author
Desmond J. Higham is a Professor of Numerical Analysis in the School of Mathematics at the University of Edinburgh. His research interests include stochastic computation, network science, data science, and their applications to online technology and human behavior. He is a Fellow of the Royal Society of Edinburgh and of the Society for Industrial and Applied Mathematics (SIAM). In 2005, he was awarded the Dahlquist Prize from SIAM, and in 2020 he received the Shephard Prize from the London Mathematical Society. He serves as editor-in-chief of SIAM Review.
Peter E. Kloeden is retired Chair of Applied and Instrumental Mathematics at 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 Prize from SIAM in 2006. In 2014, he received a Thousand Talents Award from the government of China. He serves as co-editor-in-chief of Discrete and Continuous Dynamical Systems, Series B.
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