The Resource An introduction to stochastic processes with applications to biology, Linda J. S. Allen

An introduction to stochastic processes with applications to biology, Linda J. S. Allen

Label
An introduction to stochastic processes with applications to biology
Title
An introduction to stochastic processes with applications to biology
Statement of responsibility
Linda J. S. Allen
Creator
Subject
Genre
Language
eng
Summary
"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"--
Assigning source
Provided by publisher
Cataloging source
DLC
http://library.link/vocab/creatorName
Allen, Linda J. S
Illustrations
illustrations
Index
index present
LC call number
QA274
LC item number
.A63 2011
Literary form
non fiction
Nature of contents
bibliography
http://library.link/vocab/subjectName
  • Stochastic Processes
  • Stochastic processes
  • Biomathematics
  • MATHEMATICS / Applied
  • MATHEMATICS / Probability & Statistics / Bayesian Analysis
  • Biomathematics
  • Stochastic processes
  • Stochastischer Prozess
  • Biologie
  • Stochastischer Prozess
Label
An introduction to stochastic processes with applications to biology, Linda J. S. Allen
Instantiates
Publication
Bibliography note
Includes bibliographical references and index
Contents
  • Basic Probability Concepts
  • 1.2.2.
  • Probability Distributions
  • 1.2.3.
  • Expectation
  • 1.2.4.
  • Multivariate Distributions
  • 1.3.
  • Generating Functions
  • 1.4.
  • Machine generated contents note:
  • 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.
  • 1.
  • 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.
  • Review of Probability Theory and an Introduction to Stochastic Processes
  • 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.
  • 1.1.
  • Stationary Probability Distribution
  • Introduction
  • 1.2.
  • Brief Review of Probability Theory
  • 1.2.1.
  • 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
  • 2.7.
  • 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
  • Finite Markov Chains
  • 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
  • 2.7.1.
  • 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
  • Mean First Passage Time
  • 3.6.1.
  • Expected Time to Extinction
  • 2.8.
  • An Example: Genetics Inbreeding Problem
  • 2.9.
  • Monte Carlo Simulation
  • 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
  • 3.7.
  • 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
  • Logistic Growth Process
  • 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
  • 3.8.
  • 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
  • Quasistationary Probability Distribution
  • 4.8.
  • Exercises for Chapter 4
  • 4.9.
  • References for Chapter 4
  • 5.
  • Continuous-Time Markov Chains
  • 5.1.
  • Introduction
  • 3.9.
  • SIS Epidemic Model
  • 3.9.1.
  • Deterministic Model
  • 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
  • 5.2.
  • 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
  • Definitions and Notation
  • 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
  • 5.3.
  • 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
  • The Poisson Process
  • 6.5.
  • Queueing Process
  • 6.6.
  • Population Extinction
  • 5.4.
  • Generator Matrix Q
  • 5.5.
  • Embedded Markov Chain and Classification of States
  • 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
  • 6.7.
  • 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
  • First Passage Time
  • 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
  • 6.7.1.
  • 7.4.
  • Multivariate Processes
  • 7.5.
  • Enzyme Kinetics
  • 7.5.1.
  • Deterministic Model
  • 7.5.2.
  • Stochastic Model
  • 7.6.
  • SIR Epidemic Process
  • Definition and Computation
  • 7.6.1.
  • Deterministic Model
  • 7.6.2.
  • Stochastic Model
  • 7.6.3.
  • Final Size
  • 6.7.2.
  • Summary of First Passage Time
  • 6.8.
  • Logistic Growth Process
  • 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
  • 7.6.4.
  • 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
  • Duration
  • 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
  • 7.7.
  • 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
  • Competition Process
  • 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
  • 7.7.1.
  • Deterministic Model
  • 7.7.2.
  • Stochastic Model
  • 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
  • 9.1.
  • 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
  • Introduction
  • 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
  • 9.2.
  • A.3.
  • Chapter 3
  • A.4.
  • Chapter 4
  • A.5.
  • Chapter 5
  • A.6.
  • Chapter 6
  • A.7.
  • Chapter 7
  • Multivariate Processes
  • A.8.
  • Chapter 8
  • A.9.
  • Chapter 9
  • 9.3.
  • Derivation of Ito SDEs
  • 9.4.
  • Scalar Ito SDEs for Populations
Dimensions
25 cm.
Edition
2nd ed.
Extent
xxiv, 466 p.
Isbn
9781439818824
Isbn Type
(hardback)
Lccn
2010043676
Other physical details
ill.
System control number
  • (OCoLC)615883171
  • (OCoLC)ocn615883171
Label
An introduction to stochastic processes with applications to biology, Linda J. S. Allen
Publication
Bibliography note
Includes bibliographical references and index
Contents
  • Basic Probability Concepts
  • 1.2.2.
  • Probability Distributions
  • 1.2.3.
  • Expectation
  • 1.2.4.
  • Multivariate Distributions
  • 1.3.
  • Generating Functions
  • 1.4.
  • Machine generated contents note:
  • 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.
  • 1.
  • 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.
  • Review of Probability Theory and an Introduction to Stochastic Processes
  • 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.
  • 1.1.
  • Stationary Probability Distribution
  • Introduction
  • 1.2.
  • Brief Review of Probability Theory
  • 1.2.1.
  • 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
  • 2.7.
  • 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
  • Finite Markov Chains
  • 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
  • 2.7.1.
  • 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
  • Mean First Passage Time
  • 3.6.1.
  • Expected Time to Extinction
  • 2.8.
  • An Example: Genetics Inbreeding Problem
  • 2.9.
  • Monte Carlo Simulation
  • 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
  • 3.7.
  • 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
  • Logistic Growth Process
  • 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
  • 3.8.
  • 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
  • Quasistationary Probability Distribution
  • 4.8.
  • Exercises for Chapter 4
  • 4.9.
  • References for Chapter 4
  • 5.
  • Continuous-Time Markov Chains
  • 5.1.
  • Introduction
  • 3.9.
  • SIS Epidemic Model
  • 3.9.1.
  • Deterministic Model
  • 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
  • 5.2.
  • 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
  • Definitions and Notation
  • 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
  • 5.3.
  • 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
  • The Poisson Process
  • 6.5.
  • Queueing Process
  • 6.6.
  • Population Extinction
  • 5.4.
  • Generator Matrix Q
  • 5.5.
  • Embedded Markov Chain and Classification of States
  • 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
  • 6.7.
  • 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
  • First Passage Time
  • 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
  • 6.7.1.
  • 7.4.
  • Multivariate Processes
  • 7.5.
  • Enzyme Kinetics
  • 7.5.1.
  • Deterministic Model
  • 7.5.2.
  • Stochastic Model
  • 7.6.
  • SIR Epidemic Process
  • Definition and Computation
  • 7.6.1.
  • Deterministic Model
  • 7.6.2.
  • Stochastic Model
  • 7.6.3.
  • Final Size
  • 6.7.2.
  • Summary of First Passage Time
  • 6.8.
  • Logistic Growth Process
  • 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
  • 7.6.4.
  • 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
  • Duration
  • 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
  • 7.7.
  • 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
  • Competition Process
  • 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
  • 7.7.1.
  • Deterministic Model
  • 7.7.2.
  • Stochastic Model
  • 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
  • 9.1.
  • 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
  • Introduction
  • 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
  • 9.2.
  • A.3.
  • Chapter 3
  • A.4.
  • Chapter 4
  • A.5.
  • Chapter 5
  • A.6.
  • Chapter 6
  • A.7.
  • Chapter 7
  • Multivariate Processes
  • A.8.
  • Chapter 8
  • A.9.
  • Chapter 9
  • 9.3.
  • Derivation of Ito SDEs
  • 9.4.
  • Scalar Ito SDEs for Populations
Dimensions
25 cm.
Edition
2nd ed.
Extent
xxiv, 466 p.
Isbn
9781439818824
Isbn Type
(hardback)
Lccn
2010043676
Other physical details
ill.
System control number
  • (OCoLC)615883171
  • (OCoLC)ocn615883171

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