Applied stochastic differential equations
著者
書誌事項
Applied stochastic differential equations
(Institute of Mathematical Statistics textbooks, 10)
Cambridge University Press, 2019
- : hardback
- : Paperback
大学図書館所蔵 件 / 全17件
-
該当する所蔵館はありません
- すべての絞り込み条件を解除する
注記
Includes bibliographical references (p. 281-291) and index
内容説明・目次
内容説明
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 Ito 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.
目次
- 1. Introduction
- 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
- 13. Epilogue.
「Nielsen BookData」 より