Full Description
This book presents the theory and practical applications of the Master equation approach, which provides a powerful general framework for model building in a variety of disciplines. The aim of the book is to not only highlight different mathematical solution methods, but also reveal their potential by means of practical examples.
Part I of the book, which can be used as a toolbox, introduces selected statistical fundamentals and solution methods for the Master equation. In Part II and Part III, the Master equation approach is applied to important applications in the natural and social sciences.
The case studies presented mainly hail from the social sciences, including urban and regional dynamics, population dynamics, dynamic decision theory, opinion formation and traffic dynamics; however, some applications from physics and chemistry are treated as well, underlining the interdisciplinary modelling potential of the Master equation approach.
Drawing upon the author's extensive teaching and research experience and consulting work, the book offers a valuable guide for researchers, graduate students and professionals alike.
Contents
Preface.- 1 Introduction.- 2 Statistical Fundamentals.- 3 Derivation of the Chapman-Kolmogorov Equation and the Master Equation.- 4 Solution Methods of Master Equations.- 5 Some Applications in Physics and Chemistry.- 6 The Master Equation in Dynamic Decision Theory.- 7 Applications in Population Dynamics.- 8 Migration.- 9 Urban Dynamics and Transport.
