An Introduction to Stochastic Processes with Applications to Biology - Hardcover

Allen, Linda J. S.

Hardcover

ISBN 10: 1439818827 ISBN 13: 9781439818824

Publisher: Chapman and Hall/CRC, 2010

Synopsis

An Introduction to Stochastic Processes with Applications to Biology, Second Edition presents the basic theory of stochastic processes necessary in understanding and applying stochastic methods to biological problems in areas such as population growth and extinction, drug kinetics, two-species competition and predation, the spread of epidemics, and the genetics of inbreeding. Because of their rich structure, the text focuses on discrete and continuous time Markov chains and continuous time and state Markov processes.

New to the Second Edition

• A new chapter on stochastic differential equations that extends the basic theory to multivariate processes, including multivariate forward and backward Kolmogorov differential equations and the multivariate Itô’s formula
• The inclusion of examples and exercises from cellular and molecular biology
• Double the number of exercises and MATLAB® programs at the end of each chapter
• Answers and hints to selected exercises in the appendix
• Additional references from the literature

This edition continues to provide an excellent introduction to the fundamental theory of stochastic processes, along with a wide range of applications from the biological sciences. To better visualize the dynamics of stochastic processes, MATLAB programs are provided in the chapter appendices.

About this title

About the Author

Linda J.S. Allen is a Paul Whitfield Horn Professor in the Department of Mathematics and Statistics at Texas Tech University. Dr. Allen has served on the editorial boards of the Journal of Biological Dynamics, SIAM Journal of Applied Mathematics, Journal of Difference Equations and Applications, Journal of Theoretical Biology, and Mathematical Biosciences. Her research interests encompass mathematical population biology, epidemiology, and immunology.

Review

"This book provides an excellent introduction to the basic theory of stochastic processes with regard to applications in biology. ... In this edition a new chapter on stochastic differential equations was added."
―Franziska Wandtner, Zentralblatt MATH 1263

"Instructors who are already teaching a stochastic processes course and want to introduce biological examples will find this book to be a gold mine of useful material. ... the book will be a useful addition to the library of anyone interested in stochastic processes who wants to learn more about their biological applications. I certainly learned a great deal from it!"
―Kathy Temple, MAA Reviews, January 2012

"... a good introductory textbook for junior graduate students who are interested in mathematical biology. ... First, this book is written in plain language so students with a basic probability background can easily grasp the material. ... the author obviously understands well the level of knowledge of junior graduate students so the depth of concepts is finely controlled. Second, this book covers a rich set of selected topics with a clear focus on Markov-type processes. ... Third, it must be mentioned that the author has made a great effort to encourage the use of stochastic models in practice by providing many pieces of MATLAB codes, which are usually unavailable in other books on stochastic processes. Finally, compared with the previous edition, this newly released version particularly extends the stochastic differential equation part by including the multivariate Kolmogorov equations and the Itô formula."
―Hongyu Miao, Mathematical Reviews, Issue 2011m

Edition details

• Publisher: Chapman and Hall/CRC
• Publication date: 2010
• ISBN 10: 1439818827
• ISBN 13: 9781439818824
• Binding: Hardcover
• Language: English
• Edition number: 2
• Number of pages: 496