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Workshop on Branching Processes and Their Applications

  • Conference proceedings
  • © 2010

Overview

Editors:
  1. Miguel González Velasco

    1. Fac. Ciencias, Universidad de Extremadura, Badajoz, Spain

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  2. Inés M. Puerto

    1. Fac. Ciencias, Universidad de Extremadura, Badajoz, Spain

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  3. Rodrigo Martínez

    1. Universidad de Extremadura, Plasencia, Spain

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  4. Manuel Molina

    1. Fac. Ciencias, Universidad de Extremadura, Badajoz, Spain

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  5. Manuel Mota

    1. Fac. Ciencias, Universidad de Extremadura, Badajoz, Spain

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  6. Alfonso Ramos

    1. Facultad de Veterinaria, Universidad de Extradura, Caceres, Spain

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  • Branching processes theory and their applications, mainly, on population dynamics, cell kinetics, genetics, and epidemiology
  • Includes supplementary material: sn.pub/extras

Part of the book series: Lecture Notes in Statistics (LNS, volume 197)

Part of the book sub series: Lecture Notes in Statistics - Proceedings (LNSP)

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Table of contents (20 papers)

  1. Front Matter

    Pages i-xix
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  3. Special Branching Processes

    1. Front Matter

      Pages 69-69
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    2. Approximations in population-dependent branching processes

      • Fima C. Klebaner
      Pages 71-78

    3. Extension of the problem of extinction on Galton–Watson family trees

      • George P. Yanev
      Pages 79-94

    4. Limit theorems for critical randomly indexed branching processes

      • Kosto V. Mitov, Georgi K. Mitov, Nikolay M. Yanev
      Pages 95-108

    5. Renewal measure density for distributions with regularly varying tails of order a α ∈ (0,½]

      • Valentin Topchii
      Pages 109-118

  4. Limit Theorems and Statistics

    1. Front Matter

      Pages 119-119
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    2. Approximation of a sum of martingale differences generated by a bootstrap branching process

      • Ibrahim Rahimov
      Pages 121-133

    3. Critical branching processes with immigration

      • Márton Ispány, Gyula Pap
      Pages 135-146

    4. Weighted conditional least squares estimation in controlled multitype branching processes

      • Miguel González, Inés M. del Puerto
      Pages 147-155

  5. Applications in Cell Kinetics and Genetics

    1. Front Matter

      Pages 157-157
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    2. Branching processes in cell proliferation kinetics

      • Nikolay M. Yanev
      Pages 159-178

    3. Griffiths–Pakes branching process as a model for evolution of Alu elements

      • Marek Kimmel, Matthias Mathaes
      Pages 179-189

    4. Parametric inference for Y-linked gene branching models: Expectation-maximization method

      • Miguel González, Cristina Gutiérrez, Rodrigo Martínez
      Pages 191-204

  6. Applications in Epidemiology

    1. Front Matter

      Pages 205-205
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Keywords

About this book

One of the charms of mathematics is the contrast between its generality and its applicability to concrete, even everyday, problems. Branching processes are typical in this. Their niche of mathematics is the abstract pattern of reproduction, sets of individuals changing size and composition through their members reproducing; in other words, what Plato might have called the pure idea behind demography, population biology, cell kinetics, molecular replication, or nuclear ?ssion, had he known these scienti?c ?elds. Even in the performance of algorithms for sorting and classi?cation there is an inkling of the same pattern. In special cases, general properties of the abstract ideal then interact with the physical or biological or whatever properties at hand. But the population, or bran- ing, pattern is strong; it tends to dominate, and here lies the reason for the extreme usefulness of branching processes in diverse applications. Branching is a clean and beautiful mathematical pattern, with an intellectually challenging intrinsic structure, and it pervades the phenomena it underlies.

Editors and Affiliations

  • Fac. Ciencias, Universidad de Extremadura, Badajoz, Spain

    Miguel González Velasco, Inés M. Puerto, Manuel Molina, Manuel Mota

  • Universidad de Extremadura, Plasencia, Spain

    Rodrigo Martínez

  • Facultad de Veterinaria, Universidad de Extradura, Caceres, Spain

    Alfonso Ramos

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