Multiple space-time scale analysis for interacting branching models

Electronic Journal of Probability

Volumn 1, Issue , 1996, Pages 1-84

  Dawson, Donald A ^a   Greven, Andreas ^b  

^a FIELDS INSTITUTE   (Canada)

^b UNIVERSITY OF ERLANGEN NUREMBERG   (Germany)

Author keywords

Branching processes; Historical processes; Interacting diffusions; Renormalization; Super random walk

Indexed keywords

EID: 0001790685     PISSN: None     EISSN: 10836489     Source Type: Journal    
DOI: 10.1214/EJP.v1-14     Document Type: Article

References (30)

1. J. Baillon, P. Clement, A. Greven, F. den Hollander (1995). On the attracting orbit of a nonlinear transformation arising from renormalization of hierarchically interacting diffusions: The compact case. Canadian Journal of Mathematics 47, 3-27. 2. The noncompact case. Manuscript 1995.
2. J.T. Cox, K. Fleischmann, A. Greven (1996). Comparison of interacting diffusions and an application to their ergodic theory. To appear Probab. Theory Rel. Fields.
3. J.T. Cox, A. Greven (1995). T. Shiga, Finite and infinite systems of interacting diffusions. Probab. Theory Rel. Fields.
4. D.A. Dawson (1993). Measure-valued Markov Processes. In: Ecole d’Ete de Prob-abilites de Saint Flour XXI, Lecture Notes in Mathematics 1541, 1-261, Springer-Verlag.
5. D.A. Dawson and A. Greven (1993a). Multiple time scale analysis of hierarchically interacting systems. In: A Festschrift to honor G. Kallianpur, 41-50, Springer-Verlag.
6. D.A. Dawson and A. Greven (1993b). Multiple time scale analysis of interacting diffusions. Probab. Theory Rel. Fields 95, 467-508.
7. D.A. Dawson and A. Greven (1993c). Hierarchical models of interacting diffusions: multiple time scale phenomena. Phase transition and pattern of cluster-formation. Probab. Theory Rel. Fields, 96, 435-473.
8. D.A. Dawson and P. March (1995). Resolvent estimates for Fleming-Viot operators and uniqueness of solutions to related martingale problems, J. Funct. Anal. 132, 417-472.
9. D.A. Dawson, A. Greven, J. Vaillancourt (1995). Equilibria and Quasiequilibria for Infinite Collections of Interacting Fleming-Viot processes. Transactions of the American Math. Society, volume 347, no. 7, 2277-2360.
10. D.A. Dawson and E.A. Perkins (1991). Historical Processes, Memoirs of the A.M.S. 454.
11. P. Donnelly and T. G. Kurtz (1991). A countable representation of the Fleming-Viot measure-valued diffusion, preprint.
12. J.L. Doob (1984). Classical Potential Theory and Its Probabilistic Counterpart, Springer-Verlag.
13. R. Durrett (1979). An infinite particle system with additive interactions, Adv. Appl. Probab. 11, 355-383.
14. R. Durrett (1993). Ten Lectures on Particle Systems, In: Ecole d’Ete de Probabilites de Saint Flour XXIII, Lecture Notes in Mathematics, Springer-Verlag.
15. R. Durrett and C. Neuhauser (1993). Particle systems and reaction diffusion equations, Ann. Probab., to appear.
16. W. Feller (1992). An Introduction to Probability Theory and its Applications Vol. II, Wiley & Sons.
17. J. Fleischmann (1978). Limiting distributions for branching random fields, Trans. Amer. Math. Soc. 239, 353-389.
18. K. Fleischmann and A. Greven (1994). Diffusive clustering in an infinite system of hierarchically interacting diffusions. Probab. Theory Rel. Fields 1994, 98, 517-566.
19. G. Gauthier (1994). Multilevel systems of bilinear stochastic differential equations. Preprint: Technical Report Series of the Laboratory for Research in Statistics and Probability, No. 254
20. L.G. Gorostiza and A. Wakolbinger (1992) Convergence to equilibrium of critical branching particle systems and superprocesses and related nonlinear partial differential equations, Acta Appl. Math. 27, 269-291.
21. P. Jagers (1975). Branching Processes with Biological Applications. J. Wiley.
22. O. Kallenberg (1976). Random Measures, Akademie-Verlag and Academic Press.
23. J.F.C. Kingman (1980). Mathematics of Genetic Diversity, SIAM, Philadelphia.
24. J.F.C. Kingman (1993) Poisson Processes, Clarendon Press, Oxford.
25. A. Klenke (1995). Different clustering regimes in systems of hierarchically interacting diffusions. To appear Ann. of Probability.
26. J. Lamperti and P. Ney (1968). Conditioned branching processes and their limiting diffusions, TPA 13, 128-139.
27. P.A.P. Moran (1968). An Introduction to Probability Theory, Clarendon Press, Oxford.
28. S. Sawyer and J. Felsenstein (1983). Isolation by distance in a hierarchically clustered population, J. Appl. Prob. 20, 1-10.
29. K. Shiga and A. Shimizu (1980). Infinite dimensional stochastic differential equations and their applications. J. Math. Kyoto Univ., 20, 395-415.
30. T. Shiga (1992). Ergodic theorems and exponential decay of sample paths for certain interacting diffusion systems, Osaka J. Math. 29, 789-807