| The Galton-Watson Process / Chapter I.： |
| Preliminaries / Part A.： |
| The Basic Setting / 1.： |
| Moments / 2.： |
| Elementary Properties of Generating Functions / 3.： |
| An Important Example / 4.： |
| Extinction Probability / 5.： |
| A First Look at Limit Theorems / Part B.： |
| Motivating Remarks / 6.： |
| Ratio Theorems / 7.： |
| Conditioned Limit Laws / 8.： |
| The Exponential Limit Law for the Critical Process / 9.： |
| Finer Limit Theorems / Part C.： |
| Strong Convergence in the Supercritical Case / 10.： |
| Geometric Convergence of f[subscript n](s) in the Noncritical Cases / 11.： |
| Further Ramifications / Part D.： |
| Decomposition of the Supercritical Branching Process / 12.： |
| Second Order Properties of Z[subscript n]/m[superscript n] / 13.： |
| The Q-Process / 14.： |
| More on Conditioning; Limiting Diffusions / 15.： |
| Complements and Problems I |
| Potential Theory / Chapter II.： |
| Introduction |
| Stationary Measures: Existence, Uniqueness, and Representation |
| The Local Limit Theorem for the Critical Case |
| The Local Limit Theorem for the Supercritical Case |
| Further Properties of W; A Sharp Global Limit Law; Positivity of the Density |
| Asymptotic Properties of Stationary Measures |
| Green Function Behavior |
| Harmonic Functions |
| The Space-Time Boundary |
| Complements and Problems II |
| One Dimensional Continuous Time Markov Branching Processes / Chapter III.： |
| Definition |
| Construction |
| Generating Functions |
| Extinction Probability and Moments |
| Examples: Binary Fission, Birth and Death Process |
| The Embedded Galton-Watson Process and Applications to Moments |
| Limit Theorems |
| More on Generating Functions |
| Split Times |
| Second Order Properties |
| Constructions Related to Poisson Processes |
| The Embeddability Problem |
| Complements and Problems III |
| Age-Dependent Processes / Chapter IV.： |
| Existence and Uniqueness |
| Comparison with Galton-Watson Process; Embedded Generation Process; Extinction Probability |
| Renewal Theory |
| Asymptotic Behavior of F(s, t) in the Critical Case |
| Asymptotic Behavior of F(s, t) when m[not equal]1: The Malthusian Case |
| Asymptotic Behavior of F(s, t) when m[not equal]1: Sub-Exponential Case |
| The Exponential Limit Law in the Critical Case |
| The Limit Law for the Subcritical Age-Dependent Process |
| Limit Theorems for the Supercritical Case |
| Complements and Problems IV |
| Multi-Type Branching Processes / Chapter V.： |
| Introduction and Definitions |
| Moments and the Frobenius Theorem |
| Extinction Probability and Transience |
| Limit Theorems for the Subcritical Case |
| Limit Theorems for the Critical Case |
| The Supercritical Case and Geometric Growth |
| The Continuous Time, Multitype Markov Case |
| Linear Functionals of Supercritical Processes |
| Embedding of Urn Schemes into Continuous Time Markov Branching Processes |
| The Multitype Age-Dependent Process |
| Complements and Problems V |
| Special Processes / Chapter VI.： |
| A One Dimensional Branching Random Walk |
| Cascades; Distributions of Generations |
| Branching Diffusions |
| Martingale Methods |
| Branching Processes with Random Environments |
| Continuous State Branching Processes |
| Immigration |
| Instability |
| Complements and Problems VI |
| Bibliography |
| List of Symbols |
| Author Index |
| Subject Index |
| The Galton-Watson Process / Chapter I.： |
| Preliminaries / Part A.： |
| The Basic Setting / 1.： |
| Moments / 2.： |
| Elementary Properties of Generating Functions / 3.： |
| An Important Example / 4.： |
