Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A lemma on the Galton-Watson process and some of its consequences


Author: F. Papangelou
Journal: Proc. Amer. Math. Soc. 19 (1968), 1469-1479
MSC: Primary 60.67
MathSciNet review: 0232457
Full-text PDF Free Access

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • [1] K. L. Chung, Markov chains with stationary transition probabilities, 1st ed., Springer-Verlag, Berlin, 1960. MR 0116388 (22:7176)
  • [2] W. Feller, An introduction to probability theory and its applications, Vol. 1, 2nd ed., Wiley, New York, 1957. MR 0088081 (19:466a)
  • [3] T. E. Harris, Branching processes, Springer-Verlag, Berlin, 1963. MR 0163361 (29:664)
  • [4] C. R. Heathcote, E. Seneta and D. Vere-Jones, A refinement of two theorems in the theory of branching processes, Teor. Verojatnost. i Primenen. 12 (1967), 341-346. MR 0217889 (36:978)
  • [5] A. Joffe, On the Galton-Watson branching process with mean less than one, Ann. Math. Statist. 38 (1967), 264-266. MR 0205337 (34:5166)
  • [6] S. Karlin and J. McGregor, Spectral theory of branching processes. I, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 5 (1966), 6-33. MR 0205338 (34:5167)
  • [7] H. Kesten, P. Ney and F. Spitzer, The Galton-Watson process with mean one and finite variance, Teor. Verojatnost. i Primenen. 11 (1966), 579-611. MR 0207052 (34:6868)
  • [8] A.N. Kolmogorov, Zur Lösung einer biologischen Aufgabe, Izv. Naučn.-Issled. Inst. Mat. i Meh. Tomsk. Gosudarstv. Univ. 2 (1938), 1-6.
  • [9] F. Papangelou, Strong ratio limits, $ R$-recurrence and mixing properties of discrete parameter Markov processes, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 8 (1967), 259-297. MR 0226728 (37:2315)
  • [10] E. Seneta, The Galton-Watson process with mean one, J. Appl. Probability 4 (1967), 489-495. MR 0228075 (37:3659)
  • [11] E. Seneta and D. Vere-Jones, On quasi-stationary distributions in discrete-time Markov chains with a denumerable infinity of states, J. Appl. Probability 3 (1966), 403-434. MR 0207047 (34:6863)
  • [12] D. Vere-Jones, Ergodic properties of non-negative matrices. I, Pacific J. Math. 22 (1967), 361-386. MR 0214145 (35:4996)
  • [13] A. M. Yaglom, Certain limit theoerms of the theory of branching random processes, Dokl. Akad. Nauk SSSR 56 (1947), 795-798. (Russian) MR 0022045 (9:149e)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 60.67

Retrieve articles in all journals with MSC: 60.67


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1968-0232457-5
Article copyright: © Copyright 1968 American Mathematical Society