Branching Processes and Their Applications

Editors: Inés M. del Puerto, Miguel González, Cristina Gutiérrez, Rodrigo Martínez, Carmen Minuesa, Manuel Molina, Manuel Mota, Alfonso Ramos



Represents a valuable reference on branching processes theory

Covers the most relevant and new models in branching processes theory, including both probabilistic and statistical developments

Describes the most recent applications of branching models in fields such as population dynamics, epidemiology, cell populations and genetics

This volume gathers papers originally presented at the 3rd Workshop on Branching Processes and their Applications (WBPA15), which was held from 7 to 10 April 2015 in Badajoz, Spain (http://branching.unex.es/wbpa15/index.htm). The papers address a broad range of theoretical and practical aspects of branching process theory. Further, they amply demonstrate that the theoretical research in this area remains vital and topical, as well as the relevance of branching concepts in the development of theoretical approaches to solving new problems in applied fields such as Epidemiology, Biology, Genetics, and, of course, Population Dynamics.

The topics covered can broadly be classified into the following areas:
1. Coalescent Branching Processes
2. Branching Random Walks
3. Population Growth Models in Varying and Random Environments
4. Size/Density/Resource-Dependent Branching Models
5. Age-Dependent Branching Models
6. Special Branching Models
7. Applications in Epidemiology
8. Applications in Biology and Genetics

Offering a valuable reference guide to contemporary branching process theory, the book also explores many open problems, paving the way for future research.

Table of contents (19 chapters)

Front Matter

Coalescent Branching Processes
• Front Matter
• Coalescence in Branching Processes
• A Multi-Type Λ-Coalescent

Branching Random Walks
• Front Matter
• On the Number of Positive Eigenvalues of the Evolutionary Operator of Branching Random Walk
• Branching Structures Within Random Walks and Their Applications

Population Growth Models in Varying and Random Environments
• Front Matter
• Some Asymptotic Results for Strongly Critical Branching Processes with Immigration in Varying Environment
• Subcritical Branching Processes in Random Environment

Size/Density/Resource-Dependent Branching Models
• Front Matter
• The Theorem of Envelopment and Directives of Control in Resource Dependent Branching Processes
• From Size to Age and Type Structure Dependent Branching: A First Step to Sexual Reproduction in General Population Processes

Age-Dependent Branching Models
• Front Matter
• Supercritical Sevastyanov Branching Processes with Non-homogeneous Poisson Immigration
• Crump-Mode-Jagers Branching Process: A Numerical Approach

Special Branching Models
• Front Matter
• Bayesian Analysis for Controlled Branching Processes
• Recurrence and Transience of Near-Critical Multivariate Growth Models: Criteria and Examples
• The Weighted Branching Process
• A Special Family of Galton-Watson Processes with Explosions

Applications in Epidemiology
• Front Matter
• Total Progeny of Crump-Mode-Jagers Branching Processes: An Application to Vaccination in Epidemic Modelling
• Inference for Emerging Epidemics Among a Community of Households

Applications in Biology and Genetics
• Front Matter
• Extinction Probability of Some Recessive Alleles of X-Linked Genes in the Context of Two-Sex Branching Processes
• Two-Sex Branching Processes with Several Mating and Reproduction Strategies: Extinction Versus Survival
• On Two-Type Decomposable Branching Processes in Continuous Time and Time to Escape Extinction

Back Matter

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