Random Walk and Diffusion Models

This book offers an accessible introduction to random walk and diffusion models at a level consistent with the typical background of students in the life sciences. In recent decades these models have become widely used in areas far beyond their traditional origins in physics, for example, in studies of animal behavior, ecology, sociology, sports science, population genetics, public health applications, and human decision making. Developing the main formal concepts, the book provides detailed and intuitive step-by-step explanations, and moves smoothly from simple to more complex models. Finally, in the last chapter, some successful and original applications of random walk and diffusion models in the life and behavioral sciences are illustrated in detail. The treatment of basic techniques and models is consolidated and extended throughout by a set of carefully chosen exercises.

Provides an accessible introduction to random walk and diffusion models Gives detailed examples from animal studies, sports science, public health, and human decision making Aims the exposition at a level consistent with the background of students in the life sciences

Autorentext

Wolf Schwarz is a professor at the University of Potsdam where he teaches mathematical modeling and applied statistics for life scientists. He has published extensively in leading journals devoted to applied probability, statistics, and the behavioral or life sciences. His previous book 40 Puzzles and Problems in Probability and Mathematical Statistics was published by Springer in the Problem Books in Mathematics series.

Inhalt

Introduction.- Discrete random Walks.- The Correlated Random Walk.- The Diffusion Limit.- The Wiener process.- More general Diffusion Processes.- Differential Equations for Probabilities.- Applications.