Controlled Branching Processes

  • ID: 4226585
  • Book
  • 250 Pages
  • Elsevier Science and Technology
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Controlled Branching Processes provides a comprehensive discussion of the available results for discrete time branching processes with random control functions. The independence of individuals' reproduction is a fundamental assumption in the classical branching processes. Alternatively, the controlled branching processes (CBPs) allow the number of reproductive individuals in one generation to decrease or increase depending on the size of the previous generation. Generating a wide range of behaviors, the CBPs have been successfully used as modeling tools in diverse areas of applications.

  • Presents a comprehensive analysis of the evolution of discrete branching populations with random control of the number of productive individuals
  • Develops models of populations subject to simultaneous multiple immigrations and emigration and shows how these can be used to produce a model with any desired equilibrium distribution
  • Studies discrete series of events that can arise in the process of monitoring one population and how the statistics of these events can be characterized
  • Presents methods for numerical simulation of dynamic populations, giving examples of algorithms that can be used to simulate most of the processes considered in the book, as well as computational intensive methods for estimating the main characteristics of these processes
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1. Introduction
2. Classical Branching Processes
3. Branching Processes with Migration
4. Controlled Branching Processes : Extinction
5. Controlled Branching Processes : Limit Theorems
6. Multiple Controlled Branching Processes
7. Modified Controlled Branching Processes
8. Statistics of CBP : Frequentist approach
9. Statistics of CBP : Bayesian approach
10. Historical Remarks
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González Velasco, Miguel
Miguel Gonzalez Velasco obtained his Ph.D. in Mathematical Sciences in 1994. He's an associate professor in the department of Mathematics at the University of Extremadura since 1998. His research interests include the modelization through Markov chains, the study of the probabilistic and inferential theory on branching processes and its application on genetics, epidemiology and population dynamics; and the application of statistical methodologies in fields as biology or medicine.
Garcia del Puerto, Ines Maria
Ines Maria Del Puerto Garcia has a PhD in Mathematical Sciences since November, 2002 by University of Extremadura, Spain. She is Associate Professor in the Department of Mathematics at University of Extremadura in Spain since 2008. Her research interests include the study of the probabilistic and inferential theory on branching processes.
Yanev Petrov, George
Georges Yanev is an associate professor at Texas Rio Grande Valley University. Since 2012 he's also an associate professor at the University of Texas - Pan American. He obtained he's PhD In mathematics in 2001.
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