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Journal of Applied Mathematics
Volume 2014 (2014), Article ID 364372, 4 pages
http://dx.doi.org/10.1155/2014/364372
Research Article

A Weak Limit Theorem for Galton-Watson Processes in Varying Environments

School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China

Received 28 March 2014; Accepted 22 July 2014; Published 12 August 2014

Academic Editor: Chong Lin

Copyright © 2014 Zhenlong Gao and Yanhua Zhang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. O. Zeitouni, “Random walks in random environment,” in Lectures on Probability Theory and Statistics, J. Picard, Ed., vol. 1837, pp. 189–312, 2004. View at Google Scholar
  2. W. L. Smith, “Necessary conditions for almost sure extinction of a branching process with random environment,” Annals of Mathematical Statistics, vol. 39, no. 6, pp. 2136–2140, 1968. View at Publisher · View at Google Scholar · View at MathSciNet
  3. W. L. Smith and W. E. Wilkinson, “On branching processes in random environments,” Annals of Mathematical Statistics, vol. 40, no. 3, pp. 814–827, 1969. View at Publisher · View at Google Scholar · View at MathSciNet
  4. K. B. Athreya and S. Karlin, “On branching processes with random environments. I: extinction probabilities,” Annals of Mathematical Statistics, vol. 42, pp. 1499–1520, 1971. View at Publisher · View at Google Scholar · View at MathSciNet
  5. K. B. Athreya and S. Karlin, “Branching processes with random environments, II: limit theorems,” Annals of Mathematical Statistics, vol. 42, no. 6, pp. 1843–1858, 1971. View at Publisher · View at Google Scholar · View at MathSciNet
  6. M. D. Donsker, “An invariance principle for certain probability limit theorems,” Memoirs of the American Mathematical Society, vol. 6, pp. 1–12, 1951. View at Google Scholar · View at MathSciNet
  7. D. H. Hu, “The invariance principle and its applications to branching process,” Journal of Peking University, vol. 1, pp. 1–27, 1964. View at Google Scholar
  8. D. H. Fearn, “Galton-Watson processes with generation dependence,” in Proceedings of the 6th Berkeley Symposium on Mathematical Statistics and Probability, pp. 159–172. View at MathSciNet
  9. C. C. Heyde, “A rate of convergence result for the super-critical Galton-Watson process,” Journal of Applied Probability, vol. 7, no. 2, pp. 451–454, 1970. View at Publisher · View at Google Scholar · View at MathSciNet
  10. C. C. Heyde, “Some central limit analogues for supercritical Galton-Watson processes.,” Journal of Applied Probability, vol. 8, no. 1, pp. 52–59, 1971. View at Publisher · View at Google Scholar · View at MathSciNet
  11. R. Durrett, Probability: Theory and Examples, Thomson Brooks/Cole, 3rd edition, 2005.
  12. P. Billingsley, Convergence of Probability Measures, Wiley, New York, NY, USA, 1968. View at MathSciNet