Workshop on Branching Processes and Their Applications

1. Front Matter

   Pages i-xix

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2. Population Growth Models in Random and Varying Environments

   1. Front Matter

      Pages 1-1

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   2. A refinement of limit theorems for the critical branching processes in random environment

      • Vladimir Vatutin

      Pages 3-19

   3. Branching processes in stationary random environment: The extinction problem revisited

      • Gerold Alsmeyer

      Pages 21-36

   4. Environmental versus demographic stochasticity in population growth

      • Carlos A. Braumann

      Pages 37-52

   5. Stationary distributions of the alternating branching processes

      • Penka Mayster

      Pages 53-67

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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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.

• Applications of branching processes in Epidemiology, Cell Ki
• Branching process
• Limit Theorems and Statistics in Branching Processes
• Population Growth Models in Random and Varying Environments
• Specific Branching Processes
• Two-Sex Branching Models
• statistics

• 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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