An Introduction to Stochastic Processes with Applications to Biology (Hardcover, 2)

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 X_n
Probability of Population Extinction
Mean and Variance of X_n
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
Ito Stochastic Integral
Ito 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 Ito SDEs
Scalar Ito 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.