Cover

Half-Title Page

Dedication

Title Page

Copyright Page

Contents

Foreword

Preface

1. Classical Branching Models

1.1. Bienaymé–Galton–Watson process

1.1.1. Moments and probability of extinction

1.1.2. Limit theorems

1.2. Processes with unrestricted immigration

1.2.1. Limit theorems

1.2.2. Critical process with decreasing to zero immigration

1.3. Processes with immigration after empty generation only

1.3.1. Limit theorems

1.3.2. Critical process with decreasing to zero immigration

1.4. Background and bibliographical notes

2. Branching Processes with Migration

2.1. Galton–Watson process with migration

2.2. Limit theorems

2.2.1. Non-critical processes

2.2.2. Critical processes with non-negative migration mean

2.2.3. Critical processes with negative migration mean

2.3. Regeneration and migration

2.3.1. Alternating regenerative processes

2.3.2. An extension of Galton–Watson processes with migration

2.4. Background and bibliographical notes

3. CB Processes: Extinction

3.1. Definition of processes and basic properties

3.1.1. Basic properties

3.1.2. Probability generating functions and moments

3.2. Extinction probability

3.2.1. Subcritical processes

3.2.2. Supercritical processes

3.2.3. Critical processes

3.3. Background and bibliographical notes

4. CB Processes: Limit Theorems

4.1. Subcritical processes

4.2. Critical processes

4.2.1. Extinction is not certain

4.2.2. Extinction is certain

4.2.3. Feller diffusion approximation

4.3. Supercritical processes

4.3.1. Almost sure convergence

4.3.2. L1–convergence

4.3.3. L2–convergence

4.4. Background and bibliographical notes

5. Statistics of CB Processes

5.1. Maximum likelihood estimation

5.1.1. MLE based on entire family tree up to nth generation

5.1.2. EM algorithms for incomplete data

5.1.3. Simulated example

5.2. Conditional weighted least squares estimation

5.2.1. Subcritical processes

5.2.2. Critical processes

5.2.3. Supercritical processes

5.3. Minimum disparity estimation

5.4. Bayesian inference

5.4.1. Estimation based on entire family tree up to nth generation

5.4.2. MCMC algorithms for incomplete data

5.5. Background and bibliographical notes

Appendices

Appendix 1: Limit Theorems for Martingales

Appendix 2: Some Classical Theorems

Appendix 3: Auxiliaries

Appendix 4: Simulated Data for the Examplein Chapter 5

Bibliography

Index

Other titles from iSTE in Mathematics and Statistics

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