Stochastic differential equations are differential equations whose solutions are stochastic processes. They exhibit appealing mathematical properties that are useful in modeling uncertainties and noisy phenomena in many disciplines. This book is motivated by applications of stochastic differential equations in target tracking and medical technology and, in particular, their use in methodologies such as filtering, smoothing, parameter estimation, and machine learning. It builds an intuitive hands-on understanding of what stochastic differential equations are all about, but also covers the essentials of Itô calculus, the central theorems in the field, and such approximation schemes as stochastic Runge–Kutta. Greater emphasis is given to solution methods than to analysis of theoretical properties of the equations. The book's practical approach assumes only prior understanding of ordinary differential equations. The numerous worked examples and end-of-chapter exercises include application-driven derivations and computational assignments. MATLAB/Octave source code is available for download, promoting hands-on work with the methods.Read more
- Contains worked examples and numerical simulation studies in each chapter which make ideas concrete
- Includes downloadable MATLAB®/Octave source code to support application and adaptation
- The gentle learning curve focuses on understanding and use rather than technical details
Reviews & endorsements
'Stochastic differential equations have long been used by physicists and engineers, especially in filtering and prediction theory, and more recently have found increasing application in the life sciences, finance and an ever-increasing range of fields. The authors provide intended users with an intuitive, readable introduction and overview without going into technical mathematical details from the often-demanding theory of stochastic analysis, yet clearly pointing out the pitfalls that may arise if its distinctive differences are disregarded. A large part of the book deals with underlying ideas and methods, such as analytical, approximative and computational, which are illustrated through many insightful examples. Linear systems, especially with additive noise and Gaussian solutions, are emphasized, though nonlinear systems are not neglected, and a large number of useful results and formulas are given. The latter part of the book provides an up to date survey and comparison of filtering and parameter estimation methods with many representative algorithms, and culminates with their application to machine learning.' Peter Kloeden, Johann Wolfgang Goethe-Universität Frankfurt am MainSee more reviews
'Overall, this is a very well-written and excellent introductory monograph to SDEs, covering all important analytical properties of SDEs, and giving an in-depth discussion of applied methods useful in solving various real-life problems.' Igor Cialenco, MathSciNet
'Chapters are rich in examples, numerical simulations, illustrations, derivations and computational assignment' Martin Ondreját, the European Mathematical Society and the Heidelberg Academy of Sciences and Humanities
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- Date Published: May 2019
- format: Paperback
- isbn: 9781316649466
- length: 326 pages
- dimensions: 228 x 152 x 18 mm
- weight: 0.47kg
- availability: Available
Table of Contents
2. Some background on ordinary differential equations
3. Pragmatic introduction to stochastic differential equations
4. Ito calculus and stochastic differential equations
5. Probability distributions and statistics of SDEs
6. Statistics of linear stochastic differential equations
7. Useful theorems and formulas for SDEs
8. Numerical simulation of SDEs
9. Approximation of nonlinear SDEs
10. Filtering and smoothing theory
11. Parameter estimation in SDE models
12. Stochastic differential equations in machine learning
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