Review of Probability Theory and an Introduction to Stochastic Processes Introduction Brief Review of Probability Theory Generating Functions Central Limit Theorem Introduction to Stochastic Processes An Introductory Example: A Simple Birth Process Discrete-Time Markov Chains Introduction Definitions and Notation Classification of States First Passage Time Basic Theorems for Markov Chains Stationary Probability Distribution Finite Markov Chains An Example: Genetics Inbreeding Problem Monte Carlo Simulation Unrestricted Random Walk in Higher Dimensions Biological Applications of Discrete-Time Markov Chains Introduction Proliferating Epithelial Cells Restricted Random Walk Models Random Walk with Absorbing Boundaries Random Walk on a Semi-Infinite Domain General Birth and Death Process Logistic Growth Process Quasistationary Probability Distribution SIS Epidemic Model Chain Binomial Epidemic Models Discrete-Time Branching Processes Introduction Definitions and Notation Probability Generating Function of Xn Probability of Population Extinction Mean and Variance of Xn Environmental Variation Multitype Branching Processes Continuous-Time Markov Chains Introduction Definitions and Notation The Poisson Process Generator Matrix Q Embedded Markov Chain and Classification of States Kolmogorov Differential Equations Stationary Probability Distribution Finite Markov Chains Generating Function Technique Interevent Time and Stochastic Realizations Review of Method of Characteristics Continuous-Time Birth and Death Chains Introduction General Birth and Death Process Stationary Probability Distribution Simple Birth and Death Processes Queueing Process Population Extinction First Passage Time Logistic Growth Process Quasistationary Probability Distribution An Explosive Birth Process Nonhomogeneous Birth and Death Process Biological Applications of Continuous-Time Markov Chains Introduction Continuous-Time Branching Processes SI and SIS Epidemic Processes Multivariate Processes Enzyme Kinetics SIR Epidemic Process Competition Process Predator-Prey Process Diffusion Processes and Stochastic Differential Equations Introduction Definitions and Notation Random Walk and Brownian Motion Diffusion Process Kolmogorov Differential Equations Wiener Process Itô Stochastic Integral Itô Stochastic Differential Equation (SDE) First Passage Time Numerical Methods for SDEs An Example: Drug Kinetics Biological Applications of Stochastic Differential Equations Introduction Multivariate Processes Derivation of Itô SDEs Scalar Itô SDEs for Populations Enzyme Kinetics SIR Epidemic Process Competition Process Predator-Prey Process Population Genetics Process Appendix: Hints and Solutions to Selected Exercises Index Exercises and References appear at the end of each chapter. m Walk Models Random Walk with Absorbing Boundaries Random Walk on a Semi-Infinite Domain General Birth and Death Process Logistic Growth Process Quasistationary Probability Distribution SIS Epidemic Model Chain Binomial Epidemic Models Discrete-Time Branching Processes Introduction Definitions and Notation Probability Generating Function of Xn Probability of Population Extinction Mean and Variance of Xn Environmental Variation Multitype Branching Processes Continuous-Time Markov Chains Introduction Definitions and Notation The Poisson Process Generator Matrix Q Embedded Markov Chain and Classification of States Kolmogorov Differential Equations Stationary Probability Distribution Finite Markov Chains Generating Function Technique Interevent Time and Stochastic Realizations Review of Method of Characteristics Continuous-Time Birth and Death Chains Introduction General Birth and Death Process Stationary Probability Distribution Simple Birth and Death Processes Queueing Process Population Extinction First Passage Time Logistic Growth Process Quasistationary Probability Distribution An Explosive Birth Process Nonhomogeneous Birth and Death Process Biological Applications of Continuous-Time Markov Chains Introduction Continuous-Time Branching Processes SI and SIS Epidemic Processes Multivariate Processes Enzyme Kinetics SIR Epidemic Process Competition Process Predator-Prey Process Diffusion Processes and Stochastic Differential Equations Introduction Definitions and Notation Random Walk and Brownian Motion Diffusion Process Kolmogorov Differential Equations Wiener Process Itô Stochastic Integral Itô Stochastic Differential Equation (SDE) First Passage Time Numerical Methods for SDEs An Example: Drug Kinetics Biological Applications of Stochastic Differential Equations Introduction Multivariate Processes Derivation of Itô SDEs Scalar Itô SDEs for Populations Enzyme Kinetics SIR Epidemic Process Competition Process Predator-Prey Process Population Genetics Process Appendix: Hints and Solutions to Selected Exercises Index Exercises and References appear at the end of each chapter. ed Markov Chain and Classification of States Kolmogorov Differential Equations Stationary Probability Distribution Finite Markov Chains Generating Function Technique Interevent Time and Stochastic Realizations Review of Method of Characteristics Continuous-Time Birth and Death Chains Introduction General Birth and Death Process Stationary Probability Distribution Simple Birth and Death Processes Queueing Process Population Extinction First Passage Time Logistic Growth Process Quasistationary Probability Distribution An Explosive Birth Process Nonhomogeneous Birth and Death Process Biological Applications of Continuous-Time Markov Chains Introduction Continuous-Time Branching Processes SI and SIS Epidemic Processes Multivariate Processes Enzyme Kinetics SIR Epidemic Process Competition Process Predator-Prey Process Diffusion Processes and Stochastic Differential Equations Introduction Definitions and Notation Random Walk and Brownian Motion Diffusion Process Kolmogorov Differential Equations Wiener Process Itô Stochastic Integral Itô Stochastic Differential Equation (SDE) First Passage Time Numerical Methods for SDEs An Example: Drug Kinetics Biological Applications of Stochastic Differential Equations Introduction Multivariate Processes Derivation of Itô SDEs Scalar Itô SDEs for Populations Enzyme Kinetics SIR Epidemic Process Competition Process Predator-Prey Process Population Genetics Process Appendix: Hints and Solutions to Selected Exercises Index Exercises and References appear at the end of each chapter. Epidemic Processes Multivariate Processes Enzyme Kinetics SIR Epidemic Process Competition Process Predator-Prey Process Diffusion Processes and Stochastic Differential Equations Introduction Definitions and Notation Random Walk and Brownian Motion Diffusion Process Kolmogorov Differential Equations Wiener Process Itô Stochastic Integral Itô Stochastic Differential Equation (SDE) First Passage Time Numerical Methods for SDEs An Example: Drug Kinetics Biological Applications of Stochastic Differential Equations Introduction Multivariate Processes Derivation of Itô SDEs Scalar Itô SDEs for Populations Enzyme Kinetics SIR Epidemic Process Competition Process Predator-Prey Process Population Genetics Process Appendix: Hints and Solutions to Selected Exercises Index Exercises and References appear at the end of each chapter. lt;BR>Predator-Prey Process Population Genetics Process Appendix: Hints and Solutions to Selected Exercises Index Exercises and References appear at the end of each chapter.