Time-space analysis of the cluster-formation in interacting diffusions

Electronic Journal of Probability

Volumn 1, Issue , 1996, Pages 1-46

  Fleischmann, Klaus ^a   Greven, Andreas ^b  

^a WEIERSTRASS INSTITUTE FOR APPLIED ANALYSIS AND STOCHASTICS   (Germany)

^b UNIVERSITY OF ERLANGEN NUREMBERG   (Germany)

Author keywords

Clustering; Delayed coalescing random walk with immigration; Ensemble of log coalescents; Infinite particle system; Interacting diffusion; Low dimensional systems; Transformed Fisher Wright tree

Indexed keywords

EID: 0002158520     PISSN: None     EISSN: 10836489     Source Type: Journal    
DOI: 10.1214/EJP.v1-6     Document Type: Article

References (22)

1. J.T. Cox, K. Fleischmann, and A. Greven. Comparison of interacting diffusions and application to their ergodic theory. Probab. Theory Relat. Fields, to appear 1996.
2. J.T. Cox and D. Griffeath. Occupation time limit theorem for the voter model. Ann. Probab., 11:876-893, 1983.
3. J.T. Cox and D. Griffeath. Occupation times for critical branching Brownian motions. Ann. Probab., 13(4):1108-1132, 1985.
4. J.T. Cox and D. Griffeath. Diffusive clustering in the two dimensional voter model. Ann. Probab., 14:347-370, 1986.
5. J.T. Cox and A. Greven. Ergodic theorems for infinite systems of locally interacting diffusions. Ann. Probab., 22(2):833-853, 1994.
6. d. Ann. Probab., 17(4):1333-1366, 1989.
7. D.A. Dawson. Measure-valued Markov processes. In P.L. Hennequin, editor, Ecole d’été de probabilités de Saint Flour XXI-1991, volume 1541 of Lecture Notes in Mathematics, pages 1-260, Berlin, Heidelberg, New York, 1993. Springer-Verlag.
8. D.A. Dawson and K. Fleischmann. Strong clumping of critical space-time branching models in subcritical dimensions. Stoch. Proc. Appl., 30:193-208, 1988.
9. D.A. Dawson and A. Greven. Hierarchical models of interacting diffusions: Multiple time scale phenomena, phase transitions and pattern of clusterformation. Probab. Theory Relat. Fields, 96:435-473, 1993.
10. P. Donelly and T.G. Kurtz. A countable representation of the Fleming-Viot measurevalued diffusion. Ann. Probab., to appear 1996.
11. S.N. Evans and K. Fleischmann. Cluster formation in a stepping stone model with continuous, hierarchically structered sites. WIAS Berlin, Preprint Nr. 187, 1995, Ann. Probab., to appear 1996.
12. S.N. Ethier and T.G. Kurtz. Markov Processes: Characterization and Convergence. Wiley, New York, 1986.
13. K. Fleischmann and A. Greven. Diffusive clustering in an infinite system of hierarchically interacting diffusions. Probab. Theory Relat. Fields, 98:517-566, 1994.
14. I. Iscoe. A weighted occupation time for a class of measure-valued critical branching Brownian motions. Probab. Theory Relat. Fields, 71:85-116, 1986.
15. J.F.C. Kingman. The coalescent. Stoch. Proc. Appl., 13:235-248, 1982.
16. A. Klenke. Different clustering regimes in systems of hierarchically interacting diffusions. Ann. Probab., to appear 1995.
17. T.M. Liggett. Interacting Particle Systems. Springer-Verlag, New York, 1985.
18. H. Lindqvist. Association of probability measures on partially ordered spaces. J. Multivariate Ana,lysis, 26:111-132, 1988.
19. S. Sawyer and J. Felsenstein. Isolation by distance in a hierarchically clustered population. J. Appl. Probab., 20:1-10, 1983.
20. T. Shiga. An interacting system in population genetics. J. Mat. Kyoto Univ., 20:213-242, 1980.
21. T. Shiga and A. Shimizu. Infinite-dimensional stochastic differential equations and their applications. J. Mat. Kyoto Univ., 20:395-416, 1980.
22. S. Tavare. Line-of-descent and genealogical processes, and their applications in population genetics models. Theoret. Population Biol., 26:119-164, 1984