Branching Processes and Their Applications

✍ Scribed by Inés M. del Puerto, Miguel González, Cristina Gutiérrez, Rodrigo Martínez, Carmen Minuesa, Manuel Molina, Manuel Mota, Alfonso Ramos (eds.)

• Publisher: Springer International Publishing
• Year: 2016
• Tongue: English
• Leaves: 331
• Series: Lecture Notes in Statistics 219
• Edition: 1
• Category: Library

✦ Synopsis

This volume gathers papers originally presented at the 3^rd 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

Front Matter....Pages i-xvi
Front Matter....Pages 1-1
Coalescence in Branching Processes....Pages 3-22
A Multi-Type Λ-Coalescent....Pages 23-37
Front Matter....Pages 39-39
On the Number of Positive Eigenvalues of the Evolutionary Operator of Branching Random Walk....Pages 41-55
Branching Structures Within Random Walks and Their Applications....Pages 57-73
Front Matter....Pages 75-75
Some Asymptotic Results for Strongly Critical Branching Processes with Immigration in Varying Environment....Pages 77-95
Subcritical Branching Processes in Random Environment....Pages 97-115
Front Matter....Pages 117-117
The Theorem of Envelopment and Directives of Control in Resource Dependent Branching Processes....Pages 119-136
From Size to Age and Type Structure Dependent Branching: A First Step to Sexual Reproduction in General Population Processes....Pages 137-148
Front Matter....Pages 149-149
Supercritical Sevastyanov Branching Processes with Non-homogeneous Poisson Immigration....Pages 151-166
Crump-Mode-Jagers Branching Process: A Numerical Approach....Pages 167-182
Front Matter....Pages 183-183
Bayesian Analysis for Controlled Branching Processes....Pages 185-205
Recurrence and Transience of Near-Critical Multivariate Growth Models: Criteria and Examples....Pages 207-218
The Weighted Branching Process....Pages 219-236
A Special Family of Galton-Watson Processes with Explosions....Pages 237-254
Front Matter....Pages 255-255
Total Progeny of Crump-Mode-Jagers Branching Processes: An Application to Vaccination in Epidemic Modelling....Pages 257-267
Inference for Emerging Epidemics Among a Community of Households....Pages 269-284
Front Matter....Pages 285-285
Extinction Probability of Some Recessive Alleles of X-Linked Genes in the Context of Two-Sex Branching Processes....Pages 287-305
Two-Sex Branching Processes with Several Mating and Reproduction Strategies: Extinction Versus Survival....Pages 307-317
On Two-Type Decomposable Branching Processes in Continuous Time and Time to Escape Extinction....Pages 319-329
Back Matter....Pages 331-332

✦ Subjects

Statistical Theory and Methods;Probability Theory and Stochastic Processes;Statistics for Life Sciences, Medicine, Health Sciences;Genetics and Population Dynamics