Multiple scale analysis of clusters in spatial branching models

Annals of Probability

Volumn 25, Issue 4, 1997, Pages 1670-1711

  Klenke, Achim ^a  

^a UNIVERSITY OF ERLANGEN NUREMBERG   (Germany)

Author keywords

Branching Brownian motion; Cluster phenomena; Dawson Watanabe (super) processes; Finite systems

Indexed keywords

EID: 0031321961     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/aop/1023481107     Document Type: Article

References (29)

1. BAILLON, J.-B., CLÉMENT, PH., GREVEN, A. and DEN HOLLANDER, F. (1995). On the attracting orbit of a non-linear transformation arising from renormalization of hierarchically interacting diffusions. Part I: the compact case. Canad. J. Math. 47 3-27.
2. BRAMSON, M., COX, J. T. and GREVEN, A. (1993). Ergodicity of critical spatial branching processes in low dimensions. Ann. Probab. 21 1946-1957.
3. BRAMSON, M., COX, J. T. and GREVEN, A. (1997). Invariant measures in critical spatial branching processes in high dimensions. Ann. Probab. To appear.
4. d. Ann. Probab. 17 1333-1366.
5. COX, J. T. and GREVEN, A. (1990). On the long-term behavior of some finite particle systems. Probab. Theory Related Fields 85 195-237.
6. COX, J. T. and GREVEN, A. (1991). Random walks, Brownian motion and interacting particle systems: a festschrift in honor of Frank Spitzer. Progr. Probab. 28 203-213.
7. COX, J. T. and GREVEN, A. (1994). The finite systems scheme: an abstract theorem and a new example. In Measure-Valued Processes, Stochastic Partial Differential Equations and Interacting Systems 55-67.
8. COX, J. T. and GRIFFEATH, D. (1986). Diffusive clustering in the two-dimensional voter model. Ann. Probab. 14 347-370.
9. DAWSON, D. A. (1977). The critical measure diffusion. Z. Wahrsch. Verw. Gebiete 40 125-145.
10. DAWSON, D. A. (1993). Measure-valued Markov processes. Ecole d'Eté de Probabilités de St. Flour XXI 1991. Lecture Notes in Math. 1541. Springer, Berlin.
11. DAWSON, D. A. and FLEISCHMANN, K. (1988). Strong clumping of critical space-time branching models in subcritical dimensions. Stochastic Process. Appl. 30 193-208.
12. DAWSON, D. A. and GREVEN, A. (1993a). Multiple time scale analysis of hierarchically interacting systems. In A Festschrift to Honor G. Kallianpur 41-50. Springer, New York.
13. DAWSON, D. A. and GREVEN, A. (1993b). Multiple time scale analysis of interacting diffusions. Probab. Theory Related Fields 95 467-508.
14. DAWSON, D. A., GREVEN, A. and VAILLANCOURT, J. (1995). Equilibria and quasiequilibria for infinite systems of interacting Fleming-Viot processes. Trans. Amer. Math. Soc. 347 2277-2361.
15. DURRETT, R. (1979). An infinite particle system with additive interactions. Adv. in Appl. Probab. 11 355-383.
16. FLEISCHMAN, J. (1978). Limiting distributions for branching random fields. Trans. Amer. Math. Soc. 239.
17. FLEISCHMANN, K. and GREVEN, A. (1994). Diffusive clustering in an infinite system of hierarchically interacting diffusions. Probab. Theory Related Fields 98 517-566.
18. FLEISCHMANN, K. and GREVEN, A. (1996). Time-space analysis of the cluster-formation in interacting diffusions. EJP 1, Paper 6, 1-46.
19. GOROSTIZA, L. G., ROELLY, S. and WAKOLBINGER, A. (1992). Persistence of critical multitype particle systems and measure branching processes. Probab. Theory Related Fields 92 313-335.
20. GOROSTIZA, L. G. and WAKOLBINGER, A. (1991). Persistence criteria for a class of critical branching particle systems in continuous time. Ann. Probab. 19 266-288.
21. GOROSTIZA, L. G. and WAKOLBINGER, A. (1993). Measure-valued processes, stochastic partial differential equations and interacting systems. In Measure-Valued Processes, Stochastic Partial Differential Equations and Interacting Systems 119-137.
22. KALLENBERG, O. (1977). Stability of critical cluster fields. Math. Nachr. 77 7-47.
23. KALLENBERG, O. (1983). Random Measures. Academic Press, New York.
24. KLENKE, A. (1996). Different clustering regimes in systems of hierarchically interacting diffusions. Ann. Probab. 24 660-697.
25. KOPIETZ, A. (1995). Clusterformationen bei Wechselwirkenden Diffusionen. Diplomarbeit, Göttingen.
26. LEE, T.-Y. (1991). Conditional limit distributions of critical branching Brownian motions. Ann. Probab. 19 289-311.
27. LE GALL, J.-F. (1991). Brownian excursions, trees and measure-valued branching processes. Ann. Probab. 19 1399-1439.
28. REMMERT, R. (1991). Funktionentheorie 2. Springer, Berlin
29. WINTER, A. (1995). Clusterformationen bei wechselwirkenden Feller-Diffusionen. Diplomarbeit, Berlin.