Clumping in multitype-branching trees

Advances in Applied Probability

Volumn 28, Issue 4, 1996, Pages 1034-1050

  López Mimbela, J Alfredo ^a   Wakolbinger, Anton ^b  

^a CENTRO DE INVESTIGACIÓN EN MATEMÁTICAS   (Mexico)

^b GOETHE UNIVERSITY   (Germany)

Author keywords

Ancestral process; Backward tree; Multitype branching particle systems; Nonlinear evolution systems

Indexed keywords

EID: 3042722858     PISSN: 00018678     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0001867800027543     Document Type: Article

References (16)

1. ALDOUS, D. (1989) Probability Approximations via the Poisson Clumping Heuristic. Springer, New York.
2. CHAUVIN, B., ROUAULT, A. AND WAKOLBINGER, A. (1991) Growing conditioned trees. Stoch. Proc. Appl. 39, 117-130.
3. DAWSON, D. A. (1977) The critical measure diffusion process. Z. Wahrscheinlichkeitsth. 40, 125-145.
4. DAWSON, D. A. AND FLEISCHMANN, K. (1985) Critical dimension for a model of branching in a random medium. Z. Wahrscheinlichkeitsth. 70, 315-334.
5. FELLER, W. (1966) An Introduction to Probability Theory and its Applications. Vol. 2. Wiley, New York.
6. GOROSTIZA, L., ROELLY, S. AND WAKOLBINGER, A. (1992) Persistence of critical multitype particle and measure branching processes. Prob. Theory Rel. Fields 92, 313-335.
7. GOROSTIZA, L. AND WAKOLBINGER, A. (1991) Persistence criteria for a class of critical branching particle systems in continuous time. Ann. Prob. 19, 266-288.
8. GOROSTIZA, L. AND WAKOLBINGER, A. (1993) Asymptotic behavior of a reaction-diffusion system. A probabilistic approach. Rand. Comput. Dynam. 1, 445-463.
9. HARRIS, TH. E. (1989) Branching Processes. Dover, New York.
10. ISCOE, I. (1986) A weighted occupation time for a class of measure-valued branching processes. Prob. Theory Rel. Fields 71, 85-116.
11. KALLENBERG, O. (1977) Stability of critical cluster fields. Math. Nachr. 77, 7-43.
12. LÓPEZ-MIMBELA, J. A. (1992) Fluctuation limits of multitype branching random fields. J. Multivar. Anal. 40, 56-83.
13. LÓPEZ-MIMBELA, J. A. AND WAKOLBINGER, A. (1994) Which critically branching populations persist? In Classical and Modern Branching Processes (IMA Volumes in Mathematics and its Applications), ed K. Athreya and P. Jagers. Springer, New York, (in press).
14. LYONS, R. (1994) Probability and Trees. Lecture notes and forthcoming book.
15. LYONS, R., PEMANTLE, R. AND PERES, Y. (1995) Conceptual proofs of L log L criteria for mean behavior of branching processes. Ann. Prob. 23, 1125-1138.
16. PAZY, A. (1983) Semigroups of Linear Operators with Applications to Partial Differential Equations. Springer, New York.