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