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Controlled Branching Processes

Controlled Branching Processes

Miguel González Velasco, Inés María Del Puerto García, George Petrov Yanev

ISBN: 978-1-786-30253-3

Mar 2018

232 pages


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The purpose of this book is to provide 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.

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1. Classical Branching Processes.

2. Branching Processes with Migration.

3. Controlled Branching Processes : Extinction.

4. Controlled Branching Processes : Limit Theorems.

5. Multiple Controlled Branching Processes.

6. Modified Controlled Branching Processes.

7. Statistics of CBP : Frequentist approach.

8. Statistics of CBP : Bayesian approach.

9. Historical Remarks.