08448nam a22003974a 4500 16778 16778 16528275 BD-KhUET 20180909153947.0 180909s2011 flua b 001 0 eng 2010043676 GBB060839 bnb 015551232 Uk 9781439818824 (hardback) 1439818827 (hardback) (OCoLC)ocn615883171 DLC DLC YDX BD-KhUET 519.23 22 Allen, Linda J. S. An introduction to stochastic processes with applications to biology / Linda J. S. Allen. 2nd ed. Boca Raton, FL : Chapman & Hall/CRC, c2011. xxiv, 466 p. : ill. ; 25 cm. Includes bibliographical references and index. Machine generated contents note: 1. Review of Probability Theory and an Introduction to Stochastic Processes -- 1.1. Introduction -- 1.2. Brief Review of Probability Theory -- 1.2.1. Basic Probability Concepts -- 1.2.2. Probability Distributions -- 1.2.3. Expectation -- 1.2.4. Multivariate Distributions -- 1.3. Generating Functions -- 1.4. Central Limit Theorem -- 1.5. Introduction to Stochastic Processes -- 1.6. An Introductory Example: A Simple Birth Process -- 1.7. Exercises for Chapter 1 -- 1.8. References for Chapter 1 -- 1.9. Appendix for Chapter 1 -- 1.9.1. Probability Distributions -- 1.9.2. MATLAB® and FORTRAN Programs -- 1.9.3. Interevent Time -- 2. Discrete-Time Markov Chains -- 2.1. Introduction -- 2.2. Definitions and Notation -- 2.3. Classification of States -- 2.4. First Passage Time -- 2.5. Basic Theorems for Markov Chains -- 2.6. Stationary Probability Distribution 2.7. Finite Markov Chains -- 2.7.1. Mean First Passage Time -- 2.8. An Example: Genetics Inbreeding Problem -- 2.9. Monte Carlo Simulation -- 2.10. Unrestricted Random Walk in Higher Dimensions -- 2.10.1. Two Dimensions -- 2.10.2. Three Dimensions -- 2.11. Exercises for Chapter 2 -- 2.12. References for Chapter 2 -- 2.13. Appendix for Chapter 2 -- 2.13.1. Proofs of Theorems 2.5 and 2.6 -- 2.13.2. Perron and Frobenius Theorems -- 2.13.3. The n-Step Transition Matrix -- 2.13.4. Genetics Inbreeding Problem -- 3. Biological Applications of Discrete-Time Markov Chains -- 3.1. Introduction -- 3.2. Proliferating Epithelial Cells -- 3.3. Restricted Random Walk Models -- 3.4. Random Walk with Absorbing Boundaries -- 3.4.1. Probability of Absorption -- 3.4.2. Expected Time until Absorption -- 3.4.3. Probability Distribution for Absorption -- 3.5. Random Walk on a Semi-Infinite Domain -- 3.6. General Birth and Death Process -- 3.6.1. Expected Time to Extinction 3.7. Logistic Growth Process -- 3.8. Quasistationary Probability Distribution -- 3.9. SIS Epidemic Model -- 3.9.1. Deterministic Model -- 3.9.2. Stochastic Model -- 3.10. Chain Binomial Epidemic Models -- 3.10.1. Greenwood Model -- 3.10.2. Reed-Frost Model -- 3.10.3. Duration and Size -- 3.11. Exercises for Chapter 3 -- 3.12. References for Chapter 3 -- 3.13. Appendix for Chapter 3 -- 3.13.1. MATLAB® Programs -- 3.13.2. Maple™ Program -- 4. Discrete-Time Branching Processes -- 4.1. Introduction -- 4.2. Definitions and Notation -- 4.3. Probability Generating Function of Xn -- 4.4. Probability of Population Extinction -- 4.5. Mean and Variance of Xn -- 4.6. Environmental Variation -- 4.7. Multitype Branching Processes -- 4.7.1. An Example: Age-Structured Model -- 4.7.2. Environmental Variation -- 4.8. Exercises for Chapter 4 -- 4.9. References for Chapter 4 -- 5. Continuous-Time Markov Chains -- 5.1. Introduction 5.2. Definitions and Notation -- 5.3. The Poisson Process -- 5.4. Generator Matrix Q -- 5.5. Embedded Markov Chain and Classification of States -- 5.6. Kolmogorov Differential Equations -- 5.7. Stationary Probability Distribution -- 5.8. Finite Markov Chains -- 5.9. Generating Function Technique -- 5.10. Interevent Time and Stochastic Realizations -- 5.11. Review of Method of Characteristics -- 5.12. Exercises for Chapter 5 -- 5.13. References for Chapter 5 -- 5.14. Appendix for Chapter 5 -- 5.14.1. Calculation of the Matrix Exponential -- 5.14.2. MATLAB® Programs -- 6. Continuous-Time Birth and Death Chains -- 6.1. Introduction -- 6.2. General Birth and Death Process -- 6.3. Stationary Probability Distribution -- 6.4. Simple Birth and Death Processes -- 6.4.1. Simple Birth -- 6.4.2. Simple Death -- 6.4.3. Simple Birth and Death -- 6.4.4. Simple Birth and Death with Immigration -- 6.5. Queueing Process -- 6.6. Population Extinction 6.7. First Passage Time -- 6.7.1. Definition and Computation -- 6.7.2. Summary of First Passage Time -- 6.8. Logistic Growth Process -- 6.9. Quasistationary Probability Distribution -- 6.10. An Explosive Birth Process -- 6.11. Nonhomogeneous Birth and Death Process -- 6.12. Exercises for Chapter 6 -- 6.13. References for Chapter 6 -- 6.14. Appendix for Chapter 6 -- 6.14.1. Generating Functions for the Simple Birth and Death Process -- 6.14.2. Proofs of Theorems 6.2 and 6.3 -- 6.14.3. Comparison Theorem -- 7. Biological Applications of Continuous-Time Markov Chains -- 7.1. Introduction -- 7.2. Continuous-Time Branching Processes -- 7.3. SI and SIS Epidemic Processes -- 7.3.1. Stochastic SI Model -- 7.3.2. Stochastic SIS Model -- 7.4. Multivariate Processes -- 7.5. Enzyme Kinetics -- 7.5.1. Deterministic Model -- 7.5.2. Stochastic Model -- 7.6. SIR Epidemic Process -- 7.6.1. Deterministic Model -- 7.6.2. Stochastic Model -- 7.6.3. Final Size 7.6.4. Duration -- 7.7. Competition Process -- 7.7.1. Deterministic Model -- 7.7.2. Stochastic Model -- 7.8. Predator-Prey Process -- 7.8.1. Deterministic Model -- 7.8.2. Stochastic Model -- 7.9. Exercises for Chapter 7 -- 7.10. References for Chapter 7 -- 7.11. Appendix for Chapter 7 -- 7.11.1. MATLAB® Programs -- 8. Diffusion Processes and Stochastic Differential Equations -- 8.1. Introduction -- 8.2. Definitions and Notation -- 8.3. Random Walk and Brownian Motion -- 8.4. Diffusion Process -- 8.5. Kolmogorov Differential Equations -- 8.6. Wiener Process -- 8.7. Ito Stochastic Integral -- 8.8. Ito Stochastic Differential Equation -- 8.9. First Passage Time -- 8.10. Numerical Methods for SDEs -- 8.11. An Example: Drug Kinetics -- 8.12. Exercises for Chapter 8 -- 8.13. References for Chapter 8 -- 8.14. Appendix for Chapter 8 -- 8.14.1. Derivation of Kolmogorov Equations -- 8.14.2. MATLAB® Program -- 9. Biological Applications of Stochastic Differential Equations 9.1. Introduction -- 9.2. Multivariate Processes -- 9.3. Derivation of Ito SDEs -- 9.4. Scalar Ito SDEs for Populations -- 9.4.1. Simple Birth and Death with Immigration -- 9.4.2. Logistic Growth -- 9.4.3. Quasistationary Density Function -- 9.5. Enzyme Kinetics -- 9.6. SIR Epidemic Process -- 9.7. Competition Process -- 9.8. Predator-Prey Process -- 9.9. Population Genetics Process -- 9.10. Exercises for Chapter 9 -- 9.11. References for Chapter 9 -- 9.12. Appendix for Chapter 9 -- 9.12.1. MATLAB® Programs -- Appendix A Hints and Solutions to Selected Exercises -- A.1. Chapter 1 -- A.2. Chapter 2 -- A.3. Chapter 3 -- A.4. Chapter 4 -- A.5. Chapter 5 -- A.6. Chapter 6 -- A.7. Chapter 7 -- A.8. Chapter 8 -- A.9. Chapter 9. "The second edition of a bestseller, this textbook delineates stochastic processes, emphasizing applications in biology. It includes MATLAB throughout the book to help with the solutions of various problems. The book is organized according to the three types of stochastic processes: discrete time Markov chains, continuous time Markov chains and continuous time and state Markov processes. It contains a new chapter on the biological applications of stochastic differential equations and new sections on alternative methods for derivation of a stochastic differential equation, data and parameter estimation, Monte Carlo simulation, and more"-- Stochastic processes. Biomathematics. ddc BK 0 0 ddc 0 1 KUETCL KUETCL GEN 2017-06-19 Trime 4773.00 0 519.23 ALL 3010053201 2018-09-09 00:00:00 01 2018-09-09 BK