Free Access
Issue
ESAIM: PS
Volume 15, 2011
Page(s) 417 - 442
DOI https://doi.org/10.1051/ps/2010011
Published online 05 January 2012
  1. K.B. Athreya and P.E. Ney, Branching Processes. Springer-Verlag (1972). [Google Scholar]
  2. N. Champagnat and S. Rœlly, Limit theorems for conditioned multitype Dawson-Watanabe processes and Feller diffusions. Electronic Journal of Probability 13 (2008) 777–810. [CrossRef] [MathSciNet] [Google Scholar]
  3. S. Dallaporta and A. Joffe, The Formula -process in a multitype branching process. Int. J. Pure Appl. Math. 42 (2008) 235–240. [Google Scholar]
  4. S.N. Ethier and T.G. Kurtz, Markov processes: characterization and convergence. Wiley (1986). [Google Scholar]
  5. S.N. Evans, Two representations of a conditioned superprocess, in Proc. R. Soc. Edinb. Sect. A 123 (1993) 959–971. [Google Scholar]
  6. W. Feller, Diffusion processes in genetics, in Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, 1950, University of California Press, Berkeley and Los Angeles (1951) 227–246. [Google Scholar]
  7. F.R. Gantmacher, Matrizentheorie. Springer-Verlag (1986). [Google Scholar]
  8. H.O. Georgii and E. Baake, Supercritical multitype branching processes: the ancestral types of typical individuals. Adv. Appl. Probab. 35 (2003) 1090–1110. [CrossRef] [Google Scholar]
  9. K. Fleischmann and U. Prehn, Ein Grenzwertsatz für subkritische Verzweigungsprozesse mit endlich vielen Typen von Teilchen. Math. Nachr. 64 (1974) 357–362. [CrossRef] [MathSciNet] [Google Scholar]
  10. K. Fleischmann and R. Siegmund-Schultze, The structure of reduced critical Galton-Watson processes. Math. Nachr. 79 (1977) 233–241. [CrossRef] [MathSciNet] [Google Scholar]
  11. P. Jagers and A.N. Lagerås, General branching processes conditioned on extinction are still branching processes. Electronic Communications in Probability 13 (2008) 540–547. [CrossRef] [MathSciNet] [Google Scholar]
  12. A. Joffe and M. Métivier, Weak convergence of sequences of semimartingales with applications to multitype branching processes. Adv. Appl. Probab. 18 (1986) 20–65. [CrossRef] [MathSciNet] [Google Scholar]
  13. A. Joffe and F. Spitzer, On multitype branching processes with Formula . J. Math. Anal. Appl. 19 (1967) 409–430. [CrossRef] [Google Scholar]
  14. K. Kawazu and S. Watanabe, Branching processes with immigration and related limit theorems. Theory Probab. Appl. 16 (1971) 34–51. [CrossRef] [Google Scholar]
  15. A.N. Kolmogorov, Zur Lösung einer biologischen Aufgabe. Comm. Math. Mech. Chebyshev Univ. Tomsk 2 (1938). [Google Scholar]
  16. A. Lambert, Quasi-stationary distributions and the continuous-state branching process conditioned to be never extinct. Electronic Journal of Probability 12 (2007) 420–446. [CrossRef] [MathSciNet] [Google Scholar]
  17. J. Lamperti and P. Ney, Conditioned branching process and their limiting diffusions. Theory Probab. Appl. 13 (1968) 126–137. [CrossRef] [Google Scholar]
  18. Y. Ogura, Asymptotic behavior of multitype Galton-Watson processes. J. Math. Kyoto Univ. 15 (1975) 251–302. [MathSciNet] [Google Scholar]
  19. S. Rœlly and A. Rouault, Processus de Dawson-Watanabe conditionné par le futur lointain. C. R. Acad. Sci. Sér. I Math. 309 (1989) 867–872. [Google Scholar]
  20. E. Seneta, Non-negative matrices – An introduction to theory and applications. Halsted Press (1973). [Google Scholar]
  21. B.A. Sewastjanow, Verzweigungsprozesse. R. Oldenbourg Verlag (1975). [Google Scholar]
  22. A.M. Yaglom, Certain limit theorems of the theory of branching random processes. Doklady Akad. Nauk SSSR (N.S.) 56 (1947) 795–798. [MathSciNet] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.