An Introduction to Stochastic Processes with Applications to Biology

ISBN-13: 9781439818824 / Angielski / Twarda / 2010 / 496 str.

Linda J. S. Allen;¬Abar;¬Abar

Opis

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 Ito's formula
• The inclusion of examples and exercises from cellular and molecular biology
• Double the number of exercises and MATLAB^(r) 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.

Spis treści

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.

O autorze

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.