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2010043676 contributor B11788991.
2010043676 created "c2011.".
2010043676 date "2011".
2010043676 date "c2011.".
2010043676 dateCopyrighted "c2011.".
2010043676 description "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".
2010043676 description "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".
2010043676 description "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".
2010043676 description "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".
2010043676 description "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".
2010043676 description "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.".
2010043676 description "Includes bibliographical references and index.".
2010043676 description "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".
2010043676 extent "xxiv, 466 p. :".
2010043676 identifier "1439818827 (hardback)".
2010043676 identifier "9781439818824 (hardback)".
2010043676 issued "2011".
2010043676 issued "c2011.".
2010043676 language "eng".
2010043676 publisher "Boca Raton, FL : Chapman & Hall/CRC,".
2010043676 subject "519.2/3 22".
2010043676 subject "Biomathematics.".
2010043676 subject "QA274 .A63 2011".
2010043676 subject "Stochastic processes.".
2010043676 tableOfContents "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".
2010043676 tableOfContents "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".
2010043676 tableOfContents "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".
2010043676 tableOfContents "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".
2010043676 tableOfContents "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".
2010043676 tableOfContents "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.".
2010043676 tableOfContents "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".
2010043676 title "An introduction to stochastic processes with applications to biology / Linda J. S. Allen.".
2010043676 type "text".