Foreword |
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ix | |
Preface |
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xi | |
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Chapter 1 Classical Branching Models |
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1 | (42) |
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1.1 Bienayme--Galton--Watson process |
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1 | (16) |
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1.1.1 Moments and probability of extinction |
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4 | (5) |
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9 | (8) |
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1.2 Processes with unrestricted immigration |
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17 | (12) |
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21 | (4) |
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1.2.2 Critical process with decreasing to zero immigration |
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25 | (4) |
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1.3 Processes with immigration after empty generation only |
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29 | (11) |
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31 | (5) |
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1.3.2 Critical process with decreasing to zero immigration |
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36 | (4) |
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1.4 Background and bibliographical notes |
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40 | (3) |
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Chapter 2 Branching Processes with Migration |
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43 | (22) |
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2.1 Galton--Watson process with migration |
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43 | (4) |
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47 | (8) |
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2.2.1 Non-critical processes |
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47 | (2) |
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2.2.2 Critical processes with non-negative migration mean |
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49 | (3) |
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2.2.3 Critical processes with negative migration mean |
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52 | (3) |
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2.3 Regeneration and migration |
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55 | (7) |
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2.3.1 Alternating regenerative processes |
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56 | (2) |
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2.3.2 An extension of Galton--Watson processes with migration |
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58 | (4) |
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2.4 Background and bibliographical notes |
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62 | (3) |
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Chapter 3 CB Processes: Extinction |
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65 | (30) |
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3.1 Definition of processes and basic properties |
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65 | (10) |
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69 | (4) |
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3.1.2 Probability generating functions and moments |
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73 | (2) |
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3.2 Extinction probability |
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75 | (16) |
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3.2.1 Subcritical processes |
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76 | (2) |
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3.2.2 Supercritical processes |
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78 | (6) |
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84 | (7) |
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3.3 Background and bibliographical notes |
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91 | (4) |
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Chapter 4 CB Processes: Limit Theorems |
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95 | (32) |
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4.1 Subcritical processes |
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95 | (5) |
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100 | (15) |
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4.2.1 Extinction is not certain |
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101 | (8) |
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4.2.2 Extinction is certain |
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109 | (1) |
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4.2.3 Feller diffusion approximation |
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110 | (5) |
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4.3 Supercritical processes |
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115 | (10) |
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4.3.1 Almost sure convergence |
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117 | (1) |
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118 | (3) |
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121 | (4) |
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4.4 Background and bibliographical notes |
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125 | (2) |
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Chapter 5 Statistics of CB Processes |
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127 | (52) |
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5.1 Maximum likelihood estimation |
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127 | (31) |
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5.1.1 MLE based on entire family tree up to nth generation |
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130 | (16) |
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5.1.2 EM algorithms for incomplete data |
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146 | (6) |
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152 | (6) |
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5.2 Conditional weighted least squares estimation |
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158 | (11) |
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5.2.1 Subcritical processes |
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159 | (2) |
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161 | (5) |
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5.2.3 Supercritical processes |
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166 | (3) |
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5.3 Minimum disparity estimation |
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169 | (2) |
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171 | (5) |
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5.4.1 Estimation based on entire family tree up to nth generation |
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172 | (1) |
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5.4.2 MCMC algorithms for incomplete data |
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173 | (3) |
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5.5 Background and bibliographical notes |
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176 | (3) |
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179 | (2) |
Appendix 1 |
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181 | (4) |
Appendix 2 |
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185 | (6) |
Appendix 3 |
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191 | (4) |
Appendix 4 |
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195 | (2) |
Bibliography |
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197 | (12) |
Index |
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209 | |