Controlled branching (CB) processes constitute a very large class of stochastic processes, which includes different policies of immigration and emigration. The independence of individuals’ evolution is a fundamental assumption in the classical branching processes. Alternatively, in CB processes, the number of reproductive individuals decreases or increases depending on the size of the previous generation through a random control mechanism.
The authors present a stimulating discussion and comprehensive analysis of the evolutional dynamics of the CB process, including models allowing for simultaneous multiple immigration and emigration. They present results concerning the population extinction and the limiting distributions of CB processes.
Moreover, they provide readers with an insight into both classical and computationally intensive methods for estimating the main characteristics of CB processes.
1. Classical Branching Models.
2. Branching Processes with Migration.
3. CB Processes: Extinction.
4. CB Processes: Limit Theorems.
5. Statistics of CB Processes.
Miguel González Velasco is Associate Professor at the University of Extremadura in Spain. His research interests lie in the theory of branching processes and its application to genetics, epidemiology and population dynamics.
Inés M. del Puerto García is Associate Professor at the University of Extremadura in Spain. Her research interests include the study of the probabilistic and inferential theory on branching processes.
George P. Yanev is Associate Professor at the University of Texas Rio Grande Valley in the USA. His research interests include branching processes and characterizations of probability distributions.
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