The age of a Galton-Watson population with a geometric offspring distribution

Journal of Applied Probability

Volumn 39, Issue 4, 2002, Pages 816-828

  Klebaner, F C ^a   Sagitov, S ^b  

^a MONASH UNIVERSITY   (Australia)

^b CHALMERS UNIVERSITY OF TECHNOLOGY   (Sweden)

Author keywords

Backward Galton Watson process; Critical; Geometric offspring distribution; Immigration stopped at zero; Population age; Random past

Indexed keywords

EID: 0036998566     PISSN: 00219002     EISSN: None     Source Type: Journal    
DOI: 10.1239/jap/1037816021     Document Type: Article

References (21)

1. ATHREYA, K. B. AND NEY, P. E. (1972). Branching Processes. Springer, New York.
2. ESTY, W. W. (1975). The reverse Galton-Watson process. J. Appl. Prob. 12, 574-580.
3. FELLER, W. (1971). An Introduction To Probability Theory And Its Applications, Vol. 2, 2nd edn. John Wiley, New York.
4. HEATHCOTE, C. R., SENETA, E. AND VERE-JONES, D. (1967). A refinement of two theorems in the theory of branching processes. Theory Prob. Appl. 12, 297-301.
5. IVANOFF, G. B. AND SENETA, E. (1985). The critical branching process with immigration stopped at zero. J. Appl. Prob. 22, 223-227.
6. KERSTING, G. (1986). On recurrence and transience of growth models. J. Appl. Prob. 23, 614-625.
7. KOTEESWARAN, P. (1989). Estimating the age of a Galton-Watson process with binomial offspring distribution. Stock. Analysis Appl. 7, 413-423.
8. LEVIKSON, B. (1977). The age distribution of Markov processes. J. Appl. Prob. 14, 492-506.
9. LIGGET, T. M. (1985). Interacting Particle Systems. Springer, Berlin.
10. MÖHLE, M. (1999). The concept of duality and applications to Markov processes arising in neutral population genetics models. Bernoulli 5, 761-777.
11. PAKES, A. G. (1978). On the age distribution of a Markov chain. J. Appl. Prob. 15, 65-77.
12. PAKES, A. G. (1979). The age of a Markov process. Stock. Process Appl. 8, 277-303.
13. PAKES, A. G. AND TAVARÉ, S. (1981), Comments on the age distribution of Markov processes. Adv. Appl. Prob. 13, 681-703.
14. SENETA, E. AND TAVARÉ, S. (1983). A note on the models using the branching process with immigration stopped at zero. J. Appl. Prob. 20, 11-18.
15. SEVASTSTYANOV, B. A. AND ZUBKOV, A. M. (1974). Controlled branching processes. Theory Prob. Appl. 19, 14-24.
16. STIGLER, S. M. (1970). Estimating the age of a Galton-Watson branching process. Biometrika 57, 505-512.
17. TAVARÉ, S. (1980). Time reversal and age distributions, I. Discrete-time Markov chains. J. Appl. Prob. 17, 33-46.
18. VATUTIN, V. A. (1977). A conditional limit theorem for a critical branching process with immigration. Mat. Zametki 21, 727-736.
19. YANEV, N. M. (1975). Conditions for degeneracy of φ-branching processes with random φ. Theory Prob. Appl. 20, 421-427.
20. ZUBKOV, A. M. (1972). Life-periods of a branching process with immigration. Theory Prob. Appl. 17, 174-183.
21. ZUBKOV, A. M. (1974). Analogies between Galton-Watson processes and φ-branching processes. Theory Prob. Appl. 19, 309-331.