Contents
Chapter 1. Introduction 1
Chapter 2. The Model 9
Chapter 3. Main Results 13
Chapter 4. Coupling 19
Chapter 5. Normalized Model 21
Chapter 6. Lumping 25
6.1. Distance process 25
6.2. Occupancy process 28
6.3. Invariant probability measures 30
Chapter 7. Monotonicity 33
7.1. Coupling of the lumped processes 33
7.2. Monotonicity of the model 35
Chapter 8. Stochastic Bounds 39
8.1. Lower and upper processes 39
8.2. Dynamics of the bounding processes 40
8.3. A renewal argument 41
8.4. Bounds on ν 43
Chapter 9. Birth and Death Processes 47
9.1. General formulas 47
9.2. The case of (Zt θ)t≥0 47
9.3. Persistence time 49
9.4. Invariant probability measure 51
Chapter 10. The Neutral Phase 55
10.1. Ancestral lines 55
10.2. Mutation dynamics 58
10.3. Falling to equilibrium from the left 61
10.4. Falling to equilibrium from the right 66
10.5. Discovery time 70
Chapter 11. Synthesis 79
Appendix A. Appendix on Markov Chains 81
Bibliography 85
Index 87
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