Stochastic differential equations for science and engineering
著者
書誌事項
Stochastic differential equations for science and engineering
（A Chapman & Hall book）
C&H/CRC Press, 2023
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注記
Includes bibliographical references (p. 355-360) and index
内容説明・目次
内容説明
Stochastic Differential Equations for Science and Engineering is aimed at students at the M.Sc. and PhD level. The book describes the mathematical construction of stochastic differential equations with a level of detail suitable to the audience, while also discussing applications to estimation, stability analysis, and control. The book includes numerous examples and challenging exercises. Computational aspects are central to the approach taken in the book, so the text is accompanied by a repository on GitHub containing a toolbox in R which implements algorithms described in the book, code that regenerates all figures, and solutions to exercises.
Features:
Contains numerous exercises, examples, and applications
Suitable for science and engineering students at Master's or PhD level
Thorough treatment of the mathematical theory combined with an accessible treatment of motivating examples
GitHub repository available at: https://github.com/Uffe-H-Thygesen/SDEbook and https://github.com/Uffe-H-Thygesen/SDEtools
目次
Introduction. Section I. Fundamentals. 2. Diffusive Transport and Random Walks. 3. Stochastic Experiments and Probability Spaces. 4. Brownian Motion. 5. Linear Dynamic Systems. Section II Stochastic Calculus. 6. Stochastic Integrals. 7. The Stochastic Chain Rule. 8. Existence, Uniqueness, And Numerics. 9. The Kolmogorov Equations. Section III. Applications. 10. State Estimation. 11. Expectations to The Future. 12. Stochastic Stability Theory. 13. Dynamic Optimization. 14. Perspectives.
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