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

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


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.


Corresponding author

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


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[1] Abramowitz, M., and Stegun, I. A. (eds) (1965). Handbook of Mathematical Functions. Dover, New York.
[2] Athreya, K. B., and Ney, P. E. (1972). Branching Processes. Springer, New York.
[3] Feller, W. (1939). Die Grundlagen der Volterraschen Theorie des Kampfes ums Dasein in wahrscheinlichkeitstheoretischer Behandlung. Acta Biometrika 5, 1140.
[4] Goel, N. S., and Richter-Dyn, N. (1974). Stochastic Models in Biology. Academic Press, New York.
[5] Harris, T. E. (1963). The Theory of Branching Processes. Springer, Berlin.
[6] Jagers, P. (1975). Branching Processes with Biological Applications. John Wiley, London.
[7] Kendall, D. G. (1949). Stochastic processes and population growth. J. R. Statist. Soc. B 11, 230264.
[8] Müller, J., Kretzschmar, M., and Dietz, K. (2000). Contact tracing in deterministic and stochastic models. Math. Biosci. 164, 3964.
[9] Small, P. M. et al. (1994). The epidemiology of tuberculosis in San Francisco. New England J. Med. 330, 17031709.
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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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