Branching Processes and Related Fields
Description
This volume comprises a selection of papers originally presented at the 6th International Workshop on Branching Processes and Their Applications (IWBPA24), held from April 8 to 12, 2024, in Badajoz, Spain. The contributions cover a broad spectrum of both theoretical and applied topics within the field of branching process theory. Together, they highlight the ongoing vitality and significance of this research area-not only in advancing core mathematical theory but also in tackling emerging challenges across diverse applied fields such as Epidemiology, Biology, Genetics, and Population Dynamics.
The topics explored in this volume can be broadly categorized into the following areas:
1. Markovian and non-Markovian branching trees
2. Branching processes in Biology, Genetics, and Epidemiology
3. Multitype and infinite-type branching processes
4. Branching random walks
5. Special branching models
6. Statistical inference in branching processes
Serving as a valuable resource for current research, this volume also identifies numerous open problems, paving the way for future developments in both theoretical and applied contexts.
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Persons
The editors of this volume are faculty members in the Department of Mathematics at the University of Extremadura, Spain. They form a research group with a strong focus on the probabilistic and inferential aspects of branching processes, as well as their applications-particularly in Population Dynamics, Genetics, and Epidemiology. Their academic contributions include the supervision of numerous doctoral dissertations and the publication of a substantial body of research in the field. In addition to their research activities, they have organized six editions of the International Workshop on Branching Processes and Their Applications (IWBPA), and have participated in a wide range of national and international scientific meetings.
Content
Part I Markovian and non-Markovian branching trees.- 1 An introduction to Bienaym´e-Galton-Watson trees and their local limits.- 2 The longest branches in a non-Markovian phylogenetic tree.- 3 Limit theorems for autoregressive parameter on random trees.- Part II Branching processes in Biology, Genetics, and Epidemiology.- SIR epidemic models with short-lived mixing groups.- 4 A multitype Galton-Watson model for rejuvenating cells.- 5 Branching processes and bacterial growth.- Part III Multitype and infinite-type branching processes.- 6 Multitype Markov branching processes with nonhomogeneous immigration.- 7 A Note on the Dynamics of First Moments for an Infinite- 8 TypeBranching Process Model with Random Reproductive Rates.- Part IV Branching random walks.- 9.A semigroup approach to the study of branching random walks on a multidimensional lattice.-Part V Special branching models.- 10 Power-fractional distributions and branching processes.- 11 Coalescence in Two-Sex Branching Processes.- 12 Linear and uniform in time bound for the binary branching model with Moran type interactions.- Part VI Statistical inference in branching processes.- 13 Particle filtering methods for partially observed branching processes.