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Original Articles

Bounds for the Expected Time to Extinction and the Probability of Extinction in the Galton-Watson Process

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Pages 1698-1707 | Received 19 Sep 2011, Accepted 01 Mar 2012, Published online: 28 Mar 2014

References

  • Agresti, A. (1974). Bounds on the extinction time distribution of a branching process. Adv. Appl. Probab. 6:322–335.
  • Bhattacharjee, M.C. (1987). The time to extinction of branching process and log-convexity: l. Probab. Eng. Inform. Sci. 1:265–278.
  • Cai, J., Kalashnikov, V. (2000). NWU property of a class of random sums. J. Appl. Probab. 37:283–289.
  • Feller, W. (1968). An Introduction to Probability Theory and Its Applications. New York: John Wiley & Sons, Inc.
  • From, S.G. (2007). Some new bounds on the probability of extinction of a Galton-Watson process with numerical comparisons. Communi. Statist. Theor. Meth. 36:1993–2007.
  • Ghosh, Y.N. (2003). On the probability of extinction of a Galton-Watson process. Statist. Probab. Lett. 65:195–198.
  • Harris, T. (1963). The Theory of Branching Processes. Berlin: Springer-Verlag OHG.
  • Heathcote, C.R., Seneta, E. (1966). Inequalities for branching processes. J. Appl. Probab. 3:261–267.
  • Pellerey, F. (2007). Comparison results for branching processes in random environments. J. Appl. Probab. 44:142–150.
  • Quine, M.P. (1976). Bounds for the extinction probability of a simple branching process. J. Appl. Probab. 13:9–16.
  • Ross, S. (1996). Stochastic Processes. New York: John Wiley & Sons, Inc.
  • Seneta, E. (1967). The Galton-Watson process with mean one. J. Appl. Probab. 4:489–495.
  • Shaked, M., Shanthikumar, J.G. (2007). Stochastic Orders. New York: Springer Science+Business Media, LLC.
  • Willmot, E., Cai, J. (2001). Aging and other distributional properties of discrete compound geometric distributions. Insur. Math. Econ. 28:361379.
  • Yu, J., Pei, J. (2009). Extinction of branching processes in varying environments. Statist. Probab. Lett. 79:1872–1877.

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