Stochastic Systems (Mathematics in Science and Engineering, Volume 169)

The mathematical method is easy to describe. One constructs a mathematical model of a system or part of a system. Then one uses mathematical methods to study the equations that result. Finally, one interprets the results with respect to the original system. Content: Edited by Page iii Copyright page Page iv Dedication Page v Foreword Page xi Richard Bellman Preface Pages xiii-xvii CHAPTER 1 Green's Functions and Systems Theory Pages 1-57 CHAPTER 2 A Basic Review of the Theory of Stochastic Processes Pages 58-81 CHAPTER 3 Stochastic Operators and Stochastic Systems Pages 82-95 CHAPTER 4 Linear Stochastic Differential Equations Pages 96-151 CHAPTER 5 Nonlinear Stochastic Differential Equations Pages 152-185 CHAPTER 6 Successive Improvements Pages 186-200 CHAPTER 7 Computational Aspects and a General Method Pages 201-224 CHAPTER 8 The Deterministic Limit of Stochastic Theory Pages 225-242 CHAPTER 9 Comparisons and Relations Pages 243-256 CHAPTER 10 Stochastic Partial Differential Equations Pages 257-270 CHAPTER 11 Analytical Foundations of Stochastic Operator Equations Pages 271-304 CHAPTER 12 Applications Pages 305-324 Supplementary References Pages 325-326 Index Pages 327-331 Applies the techniques of variational calculus and stochastic analysis, like Fokker-Plank equation to various models, to produce exact or approximate solutions, or in worst case numeric procedures. This book takes up issues for the coherent phenomena in stochastic dynamical systems, described by ordinary and partial differential equations. In this book, Adomian presents a simple and yet powerful method for handling stochastic equations. It is the first systematic book of this kind.