Applied Stochastic Differential Equations
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.
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.
With this hands-on introduction readers will learn what SDEs are all about and how they should
use them in practice.