Multitype linear fractional branching processes

Journal of Applied Probability

Volumn 43, Issue 4, 2006, Pages 1091-1106

  Joffe, A ^a   Letac, G ^b,c  

^a UNIVERSITÉ DE MONTRÉAL   (Canada)

^b UNIVERSITÉ PAUL SABATIER   (France)

^c INSTITUT DE MATHÉMATIQUES DE TOULOUSE   (France)

Author keywords

Linear fractional birth law; Multitype branching

Indexed keywords

EID: 33947200206     PISSN: 00219002     EISSN: None     Source Type: Journal    
DOI: 10.1239/jap/1165505210     Document Type: Article

References (11)

1. ATHREYA, K. B. AND NEY, P. E. (1972). Branching Processes. Springer, Berlin.
2. GORYAINOV, V. V. (1993). Fractional iteration of probability-generating functions and imbedding discrete branching processes into continuous processes. Mat. Sb. 184, 55-74 (in Russian).
3. English translation: Russian Acad. Sci. Sb. Math. 79, 47-61, 1994.
4. GORYAINOV, V. V. (1995). Semigroups of probability generating function, and infinitely splittable functions. Theory Random Process. V.1 17, 2-9.
5. GORYAINOV, V. V. (2002). Koenigs function and fractional iterates of probability generating functions. Sb. Math. 193, 1009-1025.
6. GREY, D. R. (1975). Two necessary conditions for erabeddability of a Gallon-Watson branching process. Math. Proc. Camb. Phil. Soc. 78, 339-343.
7. HARRIS, T. E. (1963). The Theory of Branching Processes. Springer, Berlin.
8. KARLIN, S. AND MCGREGOR, J. (1968a). Embeddability of discrete time simple branching processes into continuous time branching processes. Trans. Amer. Math. Soc. 132, 115-136.
9. KARLIN, S. AND MCGREGOR, J. (1968b). Embedding iterates of analytic functions with two fixed points into continuous groups. Trans. Amer. Math. Soc. 132, 137-145.
10. POLLAK, E. (1974). Survival probabilities and extinction times for some multitype branching processes. Adv. Appl. Prob. 6, 446-462.
11. TOULOUSE, P. S. (1999). Thèmes de Probabilités et Statistique. Dunod, Paris.