Applied Stochastic Differential Equations (Institute of Mathematical Statistics Textbooks, Series Number 10)

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. 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 Cover......Page 1 Front Matter......Page 3 INSTITUTE OF MATHEMATICAL STATISTICSTEXTBOOKS......Page 4 Applied Stochastic Differential Equations......Page 5 Copyright......Page 6 Contents......Page 7 Preface......Page 11 1 Introduction......Page 13 2 Some Background on Ordinary DifferentialEquations......Page 16 3 Pragmatic Introduction to StochasticDifferential Equations......Page 35 4 Itô Calculus and Stochastic DifferentialEquations......Page 54 5 Probability Distributions and Statistics ofSDEs......Page 71 6 Statistics of Linear Stochastic DifferentialEquations......Page 89 7 Useful Theorems and Formulas for SDEs......Page 110 8 Numerical Simulation of SDEs......Page 138 9 Approximation of Nonlinear SDEs......Page 177 10 Filtering and Smoothing Theory......Page 209 11 Parameter Estimation in SDE Models......Page 246 12 Stochastic Differential Equations in MachineLearning......Page 263 13 Epilogue......Page 289 References......Page 293 Symbols and Abbreviations......Page 305 List of Examples......Page 317 List of Algorithms......Page 321 Index......Page 323 "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";Some background on ordinary differential equations -- Pragmatic introduction to stochastic differential equations -- Itô calculus and stochastic differential equations -- Probability distributions and statistics of SDEs -- Statistics of linear stochastic differential equations -- Useful theorems and formulas for SDEs -- Numerical simulation of SDEs -- Approximation of non-linear SDEs -- Filtering and smoothing theory -- Parameter estimation in SDE models -- Stochastic differential equations in machine learning This intuitive hands-on text introduces stochastic differential equations (SDEs) as motivated by applications in target tracking and medical technology, and covers their use in methodologies such as filtering, parameter estimation, and machine learning. Examples include applications of SDEs arising in physics and electrical engineering.