Introduction to Stochastic Processes with Applications to Biology

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 of Probability Theory and an Introduction to Stochastic Processes. Discrete-Time Markov Chains. Biological Applications of Discrete-Time Markov Chains. Discrete-Time Branching Processes. Continuous-Time Markov Chains. Continuous-Time Birth and Death Chains. Biological Applications of Continuous-Time Markov Chains. Diffusion Processes and Stochastic Differential Equations. Biological Applications of Stochastic Differential Equations. Appendix. Index.

"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