Discrete time branching processes in random environment /
Branching processes are stochastic processes which represent the reproduction of particles, such as individuals within a population, and thereby model demographic stochasticity. In branching processes in random environment (BPREs), additional environmental stochasticity is incorporated, meaning that...
Clasificación: | Libro Electrónico |
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Autores principales: | , |
Formato: | Electrónico eBook |
Idioma: | Inglés |
Publicado: |
London : Hoboken, NJ :
ISTE Ltd ; John Wiley & Sons, Inc.,
2017.
|
Colección: | Mathematics and statistics series (ISTE). Branching processes, branching random walks and branching particle fields set ;
v. 1. |
Temas: | |
Acceso en línea: | Texto completo (Requiere registro previo con correo institucional) |
Tabla de Contenidos:
- Cover
- Half-Title Page
- Title Page
- Copyright Page
- Contents
- Preface
- List of Notations
- 1. Branching Processes in Varying Environment
- 1.1. Introduction
- 1.2. Extinction probabilities
- 1.3. Almost sure convergence
- 1.4. Family trees
- 1.4.1. Construction of the Geiger tree
- 1.4.2. Construction of the size-biased tree T*
- 1.5. Notes
- 2. Branching Processes in Random Environment
- 2.1. Introduction
- 2.2. Extinction probabilities
- 2.3. Exponential growth in the supercritical case
- 2.4. Three subcritical regimes
- 2.5. The strictly critical case2.6. Notes
- 3. Large Deviations for BPREs
- 3.1. Introduction
- 3.2. A tail estimate for branching processes in a varying environment
- 3.3. Proof of Theorem 3.1
- 3.4. Notes
- 4. Properties of Random Walks
- 4.1. Introduction
- 4.2. Sparre-Andersen identities
- 4.3. Spitzer identity
- 4.4. Applications of Sparre-Andersen and Spitzer identities
- 4.4.1. Properties of ladder epochs and ladder heights
- 4.4.2. Tail distributions of ladder epochs
- 4.4.3. Some renewal functions
- 4.4.4. Asymptotic properties of Ln and Mn4.4.5. Arcsine law
- 4.4.6. Large deviations for random walks
- 4.5. Notes
- 5. Critical BPREs: the Annealed Approach
- 5.1. Introduction
- 5.2. Changes of measures
- 5.3. Properties of the prospective minima
- 5.4. Survival probability
- 5.5. Limit theorems for the critical case (annealed approach)
- 5.6. Environment providing survival
- 5.7. Convergence of log Zn
- 5.8. Notes
- 6. Critical BPREs: the Quenched Approach
- 6.1. Introduction
- 6.2. Changes of measures
- 6.3. Probability of survival
- 6.4. Yaglom limit theorems6.4.1. The population size at non-random moments
- 6.4.2. The population size at moments nt, 0 nt
- 6.5. Discrete limit distributions
- 6.6. Notes
- 7. Weakly Subcritical BPREs
- 7.1. Introduction
- 7.2. The probability measures P+ and Pâ#x88;#x92;
- 7.3. Proof of theorems
- 7.3.1. Proof of Theorem 7.1
- 7.3.2. Proof of Theorem 7.2
- 7.3.3. Proof of Theorem 7.3
- 7.4. Notes
- 8. Intermediate Subcritical BPREs
- 8.1. Introduction8.2. Proof of Theorems 8.1 to 8.3
- 8.3. Further limit results
- 8.4. Conditioned family trees
- 8.5. Proof of Theorem 8.4
- 8.6. Notes
- 9. Strongly Subcritical BPREs
- 9.1. Introduction
- 9.2. Survival probability and Yaglom-type limit theorems
- 9.3. Environments providing survival and dynamics of the population size
- 9.3.1. Properties of the transition matrix P*
- 9.3.2. Proof of Theorem 9.2
- 9.3.3. Proof of Theorem 9.3
- 9.4. Notes
- 10. Multi-type BPREs
- 10.1. Introduction
- 10.2. Supercritical MBPREs