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Controlled branching processes with continuous time

Part of: Markov processes Special processes

Published online by Cambridge University Press:  16 September 2021

Miguel González Open the ORCID record for Miguel González [Opens in a new window] ,
Manuel Molina Open the ORCID record for Manuel Molina [Opens in a new window] ,
Ines del Puerto Open the ORCID record for Ines del Puerto [Opens in a new window] ,
Nikolay M. Yanev  and
George P. Yanev Open the ORCID record for George P. Yanev [Opens in a new window]
Miguel González*
Affiliation:
University of Extremadura
Manuel Molina*
Affiliation:
University of Extremadura
Ines del Puerto*
Affiliation:
University of Extremadura
Nikolay M. Yanev*
Affiliation:
Bulgarian Academy of Sciences
George P. Yanev*
Affiliation:
University of Texas RGV and Bulgarian Academy of Sciences
*
*Postal address: Department of Mathematics, Faculty of Sciences, University of Extremadura, 06006 Badajoz, Spain.
*Postal address: Department of Mathematics, Faculty of Sciences, University of Extremadura, 06006 Badajoz, Spain.
*Postal address: Department of Mathematics, Faculty of Sciences, University of Extremadura, 06006 Badajoz, Spain.
*****Postal address: Department of Operations Research, Probability and Statistics, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria. Email address: [email protected]
******Postal address: The University of Texas Rio Grande Valley, School of Mathematical & Statistical Sciences, 1201 W. University Drive, Edinburg, TX 78539, USA. Email address: [email protected]
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Abstract

A class of controlled branching processes with continuous time is introduced and some limiting distributions are obtained in the critical case. An extension of this class as regenerative controlled branching processes with continuous time is proposed and some asymptotic properties are considered.

Keywords

Controlled branching processrenewal processregenerative processrandom time changelimit theorem

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60K05: Renewal theory 60J85: Applications of branching processes 60K10: Applications (reliability, demand theory, etc.)
Type
Original Article
Information
Journal of Applied Probability , Volume 58 , Issue 3 , September 2021 , pp. 830 - 848
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Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Applied Probability Trust

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