Population-size-dependent and age-dependent branching processes

Stochastic Processes and their Applications

Volumn 87, Issue 2, 2000, Pages 235-254

  Jagers, Peter ^a   Klebaner, Fima C ^b  

^a CHALMERS UNIVERSITY OF TECHNOLOGY   (Sweden)

^b UNIVERSITY OF MELBOURNE   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0041707131     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-4149(99)00111-8     Document Type: Article

References (24)

1. Athreya K.B., Ney P. Branching Processes. 1972;Springer, Berlin.
2. Borde-Boussion A.-M. Stochastic demographic models: age of a population. Stochastic Process. Appl. 35:1990;279-291.
3. Dawson, D., 1993. Measure-valued Markov Processes. Lecture Notes.
4. Dieudonné J. Foundations of Modern Analysis. 1960;Academic Press, New York.
5. Durrett, R., 1996. Probability: Theory and Examples. 2nd Edition. Duxbury Press, Belmont.
6. Ethier S.N., Kurtz T.G. Markov Processes. 1986;Wiley, New York.
7. Hamza K., Klebaner F.C. Condition for integrability of Markov chains. J. Appl. Probab. 32:1995;541-547.
8. Harris, T.E., 1963. The Theory of Branching Processes. Springer, Berlin; Dover, New York, 1989.
9. Jagers P. Branching Processes with Biological Applications. 1975;Wiley, New York.
10. Jagers P. Branching Processes at Markov Fields. Stochastic Process. Appl. 32:1989;183-242.
11. Jagers P. Coupling and population dependence in branching processes. Ann. Appl. Probab. 7:1997;281-298.
12. Jagers, P., 2000. Branching processes with dependence but homogeneous growth. Ann. Appl. Probab., in press.
13. Klebaner F.C. Geometric rate of growth in population size dependent branching processes. J. Appl. Probab. 21:1984;40-49.
14. Klebaner F.C. Geometric growth in near-supercritical population size dependent multitype Galton-Watson processes. Ann. Probab. 17(4):1989;1466-1477.
15. Klebaner F.C. Asymptotic behaviour of Markov population processes with asymptotically linear rate of change. J. Appl. Probab. 31:1994;614-625.
16. Klebaner, F.C., 1998. Introduction to Stochastic Calculus with Applications. Imperial College Press, London.
17. Métivier, M., 1987. Weak convergence of measure valued processes using Sobolev imbedding techniques. Lecture Notes in Maths., Vol. 1236, Springer, Berlin, pp. 172-183.
18. Nerman O. On the convergence of supercritical general (C-M-J) branching processes. Z. Wahrsch. Verw. Geb. 57:1981;365-395.
19. Oelschläger K. A martingale approach to the Law of Large Numbers for weakly interacting stochastic processes. Ann. Probab. 12:1984;458-479.
20. Oelschläger, K., 1990. Limit theorems for age-structured populations, Ann. Probab. 18, 290-318, 458-479.
21. Protter P. Stochastic Integration and Differential Equations. 1992;Springer, Berlin.
22. Schuh H.-J. Seneta constants for the supercritical Bellman-Harris process. Adv. Appl. Probab. 14:1982;732-751.
23. Widder D.V. The Laplace Transform. 1946;Princeton University Press, Princeton, NJ.
24. Wiener N. The Fourier Integral and Certain of Its Applications. 1933;Dover Publications, Cambridge University Press, New York, Cambridge.