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Markov branching processes with instantaneous immigration
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  • Published: June 1990

Markov branching processes with instantaneous immigration

  • A. Y. Chen1 &
  • E. Renshaw1 

Probability Theory and Related Fields volume 87, pages 209–240 (1990)Cite this article

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  • 36 Citations

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Summary

Markov branching processes with instantaneous immigration possess the property that immigration occurs immediately the number of particles reaches zero, i.e. the conditional expectation of sojourn time at zero is zero. In this paper we consider the existence and uniqueness of such a structure. We prove that if the sum of the immigration rates is finite then no such structure can exist, and we provide a necessary and sufficient condition for existence for the case in which this sum is infinite. Study of the uniqueness problem shows that for honest processes the solution is unique.

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Authors and Affiliations

  1. Department of Statistics, James Clerk Maxwell Building, King's Buildings, University of Edinburgh, Mayfield Road, EH9 3JZ, Edinburgh, UK

    A. Y. Chen & E. Renshaw

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  1. A. Y. Chen
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  2. E. Renshaw
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Chen, A.Y., Renshaw, E. Markov branching processes with instantaneous immigration. Probab. Th. Rel. Fields 87, 209–240 (1990). https://doi.org/10.1007/BF01198430

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  • Received: 03 January 1990

  • Revised: 28 June 1990

  • Issue Date: June 1990

  • DOI: https://doi.org/10.1007/BF01198430

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Keywords

  • Stochastic Process
  • Probability Theory
  • Mathematical Biology
  • Conditional Expectation
  • Sojourn Time
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