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E-grāmata: Controlled Branching Processes [Wiley Online]

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  • Formāts: 240 pages
  • Izdošanas datums: 09-Jan-2018
  • Izdevniecība: ISTE Ltd and John Wiley & Sons Inc
  • ISBN-10: 111945297X
  • ISBN-13: 9781119452973
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  • Wiley Online
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Controlled Branching ProcessesPalielināt
  • Formāts: 240 pages
  • Izdošanas datums: 09-Jan-2018
  • Izdevniecība: ISTE Ltd and John Wiley & Sons Inc
  • ISBN-10: 111945297X
  • ISBN-13: 9781119452973
Citas grāmatas par šo tēmu:
Wiley Online E-booksMore info about Wiley Online
Rokasgrāmatas mājas lapa: https://onlinelibrary.wiley.com/doi/book/10.1002/9781119452973

The purpose of this book is to provide a comprehensive discussion of the available results for discrete time branching processes with random control functions. The independence of individuals’ reproduction is a fundamental assumption in the classical branching processes. Alternatively, the controlled branching processes (CBPs) allow the number of reproductive individuals in one generation to decrease or increase depending on the size of the previous generation.

Generating a wide range of behaviors, the CBPs have been successfully used as modeling tools in diverse areas of applications.

Foreword ix
Preface xi
Chapter 1 Classical Branching Models
1(42)
1.1 Bienayme--Galton--Watson process
1(16)
1.1.1 Moments and probability of extinction
4(5)
1.1.2 Limit theorems
9(8)
1.2 Processes with unrestricted immigration
17(12)
1.2.1 Limit theorems
21(4)
1.2.2 Critical process with decreasing to zero immigration
25(4)
1.3 Processes with immigration after empty generation only
29(11)
1.3.1 Limit theorems
31(5)
1.3.2 Critical process with decreasing to zero immigration
36(4)
1.4 Background and bibliographical notes
40(3)
Chapter 2 Branching Processes with Migration
43(22)
2.1 Galton--Watson process with migration
43(4)
2.2 Limit theorems
47(8)
2.2.1 Non-critical processes
47(2)
2.2.2 Critical processes with non-negative migration mean
49(3)
2.2.3 Critical processes with negative migration mean
52(3)
2.3 Regeneration and migration
55(7)
2.3.1 Alternating regenerative processes
56(2)
2.3.2 An extension of Galton--Watson processes with migration
58(4)
2.4 Background and bibliographical notes
62(3)
Chapter 3 CB Processes: Extinction
65(30)
3.1 Definition of processes and basic properties
65(10)
3.1.1 Basic properties
69(4)
3.1.2 Probability generating functions and moments
73(2)
3.2 Extinction probability
75(16)
3.2.1 Subcritical processes
76(2)
3.2.2 Supercritical processes
78(6)
3.2.3 Critical processes
84(7)
3.3 Background and bibliographical notes
91(4)
Chapter 4 CB Processes: Limit Theorems
95(32)
4.1 Subcritical processes
95(5)
4.2 Critical processes
100(15)
4.2.1 Extinction is not certain
101(8)
4.2.2 Extinction is certain
109(1)
4.2.3 Feller diffusion approximation
110(5)
4.3 Supercritical processes
115(10)
4.3.1 Almost sure convergence
117(1)
4.3.2 L1--convergence
118(3)
4.3.3 L2--convergence
121(4)
4.4 Background and bibliographical notes
125(2)
Chapter 5 Statistics of CB Processes
127(52)
5.1 Maximum likelihood estimation
127(31)
5.1.1 MLE based on entire family tree up to nth generation
130(16)
5.1.2 EM algorithms for incomplete data
146(6)
5.1.3 Simulated example
152(6)
5.2 Conditional weighted least squares estimation
158(11)
5.2.1 Subcritical processes
159(2)
5.2.2 Critical processes
161(5)
5.2.3 Supercritical processes
166(3)
5.3 Minimum disparity estimation
169(2)
5.4 Bayesian inference
171(5)
5.4.1 Estimation based on entire family tree up to nth generation
172(1)
5.4.2 MCMC algorithms for incomplete data
173(3)
5.5 Background and bibliographical notes
176(3)
Appendices
179(2)
Appendix 1 181(4)
Appendix 2 185(6)
Appendix 3 191(4)
Appendix 4 195(2)
Bibliography 197(12)
Index 209
Inés Marķa Del Puerto Garcķa, University of Extramadura, Spain  Miguel Velasco Gonzįlez, University of Extramadura, Spain  George Yanev, University of Texas Rio Grande Valley, United States
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