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Stationary distributions of the alternating branching processes

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Workshop on Branching Processes and Their Applications

Part of the book series: Lecture Notes in Statistics ((LNSP,volume 197))

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Abstract

We consider the model of alternating branching processes, where two Markov branching processes act alternately by the random time periods of observation and treatment. Stationary distributions can be obtained by feed-back control if the observation time δ is defined by the additive functional of total progeny of the supercritical Markov branching process ξ(t), or by the explicit immigration of particles. We investigate the reproduction by n cycles and limit theorems to obtain the stationary distributions.

Mathematics Subject Classification (2000): 60J80, 60K05

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Authors and Affiliations

  1. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad.G.Bonchev Street, Bloc 8, 1113, Sofia, Bulgaria

    Penka Mayster

Authors
  1. Penka Mayster
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Correspondence to Penka Mayster .

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Editors and Affiliations

  1. Fac. Ciencias, Universidad de Extremadura, Avenida Elvas s/n, Badajoz, 06071, Spain

    Miguel González Velasco

  2. Fac. Ciencias, Universidad de Extremadura, Avenida Elvas s/n, Badajoz, 06071, Spain

    Inés M. Puerto

  3. Universidad de Extremadura, Avda. Virgen del Puerto, Plasencia, 10600, Spain

    Rodrigo Martínez

  4. Fac. Ciencias, Universidad de Extremadura, Avenida Elvas s/n, Badajoz, 06071, Spain

    Manuel Molina

  5. Fac. Ciencias, Universidad de Extremadura, Avenida Elvas s/n, Badajoz, 06071, Spain

    Manuel Mota

  6. Facultad de Veterinaria, Universidad de Extradura, Avda Universidad s/n, Caceres, 10071, Spain

    Alfonso Ramos

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Mayster, P. (2010). Stationary distributions of the alternating branching processes. In: González Velasco, M., Puerto, I., Martínez, R., Molina, M., Mota, M., Ramos, A. (eds) Workshop on Branching Processes and Their Applications. Lecture Notes in Statistics(), vol 197. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11156-3_4

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