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Family trees of continuous-time birth-and-death processes

  • Johannes Müller (a1) and Martin Möhle (a2)

Abstract

We consider a stochastic graph generated by a continuous-time birth-and-death process with exponentially distributed waiting times. The vertices are the living particles, directed edges go from mothers to daughters. The size and the structure of the connected components are investigated. Furthermore, the number of connected components is determined.

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Corresponding author

Postal address: Mathematics Institute, Munich University of Technology, Boltzmannstraße 3, D-85748 Garching, Germany. Email address: johannes.mueller@gsf.de
∗∗ Postal address: Mathematics Institute, University of Tübingen, Auf der Morgenstelle 10, D-72076 Tübingen, Germany.

References

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[8] Müller, J., Kretzschmar, M., and Dietz, K. (2000). Contact tracing in deterministic and stochastic models. Math. Biosci. 164, 3964.
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Journal of Applied Probability
  • ISSN: 0021-9002
  • EISSN: 1475-6072
  • URL: /core/journals/journal-of-applied-probability
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