This volume contains papers presented at the Workshop on Branching Processes and Their Applications (WBPA09). These papers deal with theoretical and practical aspects of branching process theory, showing it to be an area of active and interesting research. They clearly indicate the vitality of the theoretical research on this topic, as well as the importance of branching concepts in the development of theoretical approaches to solving new problems in applied fields such as Epidemiology, Cell Kinetics, Genetics, and, of course, Population Dynamics. The topics covered by the papers have been classified into the following areas:

• Population Growth Models in Random and Varying Environments
• Special Branching Processes
• Limit Theorems and Statistics
• Applications in Cell Kinetics and Genetics
• Applications in Epidemiology

• Two-Sex Branching Models

  This book represents a valuable reference on the contemporary branching processes theory, presenting also many open problems which will lead to future research.

  Zusammenfassung
  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.

  Inhalt
  Population Growth Models in Random and Varying Environments.- A refinement of limit theorems for the critical branching processes in random environment.- Branching processes in stationary random environment: The extinction problem revisited.- Environmental versus demographic stochasticity in population growth.- Stationary distributions of the alternating branching processes.- Special Branching Processes.- Approximations in population-dependent branching processes.- Extension of the problem of extinction on GaltonWatson family trees.- Limit theorems for critical randomly indexed branching processes.- Renewal measure density for distributions with regularly varying tails of order a ? ? (0,½].- Limit Theorems and Statistics.- Approximation of a sum of martingale differences generated by a bootstrap branching process.- Critical branching processes with immigration.- Weighted conditional least squares estimation in controlled multitype branching processes.- Applications in Cell Kinetics and Genetics.- Branching processes in cell proliferation kinetics.- GriffithsPakes branching process as a model for evolution of Alu elements.- Parametric inference for Y-linked gene branching models: Expectation-maximization method.- Applications in Epidemiology.- Applications of branching processes to the final size of SIR epidemics.- A branching process approach for the propagation of the Bovine Spongiform Encephalopathy in Great-Britain.- Time to extinction of infectious diseases through age-dependent branching models.- Time to extinction in a two-host interaction model for the macroparasite Echinococcus granulosus.- Two-sex Branching Models.- Bisexual branching processes with immigration depending on the number of females and males.- Two-sex branching process literature.