Liu, Huili and Zhou, Xiaowen (2012) The compact support property for the $\Lambda$-Fleming-Viot process with underlying Brownian motion. Electronic Journal of Probability, 17 . ISSN 1083-6489
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Official URL: http://dx.doi.org/10.1214/EJP.v17-1928
Abstract
Using the lookdown construction of Donnelly and Kurtz we prove that, at any fixed positive time, the $\Lambda$-Fleming-Viot process with underlying Brownian motion has a compact support provided that the corresponding $\Lambda$-coalescent comes down from infinity not too slowly. We also find both upper bound and lower bound on the Hausdorff dimension for the support.
| Divisions: | Concordia University > Faculty of Arts and Science > Mathematics and Statistics |
|---|---|
| Item Type: | Article |
| Refereed: | Yes |
| Authors: | Liu, Huili and Zhou, Xiaowen |
| Journal or Publication: | Electronic Journal of Probability |
| Date: | 2012 |
| Digital Object Identifier (DOI): | 10.1214/EJP.v17-1928 |
| ID Code: | 976832 |
| Deposited By: | Danielle Dennie |
| Deposited On: | 29 Jan 2013 14:45 |
| Last Modified: | 18 Jan 2018 17:43 |
References:
•Birkner, Matthias; Blath, Jochen. Measure-valued diffusions, general coalescents and population genetic inference. Trends in stochastic analysis, 329--363, London Math. Soc. Lecture Note Ser., 353, Cambridge Univ. Press, Cambridge, 2009. MR2562160•Birkner, Matthias; Blath, Jochen; Möhle, Martin; Steinrücken, Matthias; Tams, Johanna. A modified lookdown construction for the Xi-Fleming-Viot process with mutation and populations with recurrent bottlenecks. ALEA Lat. Am. J. Probab. Math. Stat. 6 (2009), 25--61. MR2485878
•Blath, Jochen. Measure-valued processes, self-similarity and flickering random measures. Fractal geometry and stochastics IV, 175--196, Progr. Probab., 61, Birkhäuser Verlag, Basel, 2009. MR2762677
•Dawson, Donald A.; Hochberg, Kenneth J. Wandering random measures in the Fleming-Viot model. Ann. Probab. 10 (1982), no. 3, 554--580. MR0659528
•Donnelly, Peter; Kurtz, Thomas G. A countable representation of the Fleming-Viot measure-valued diffusion. Ann. Probab. 24 (1996), no. 2, 698--742. MR1404525
•Donnelly, Peter; Kurtz, Thomas G. Genealogical processes for Fleming-Viot models with selection and recombination. Ann. Appl. Probab. 9 (1999), no. 4, 1091--1148. MR1728556
•Donnelly, Peter; Kurtz, Thomas G. Particle representations for measure-valued population models. Ann. Probab. 27 (1999), no. 1, 166--205. MR1681126
•Ethier, S. N.; Kurtz, Thomas G. Fleming-Viot processes in population genetics. SIAM J. Control Optim. 31 (1993), no. 2, 345--386. MR1205982
•Etheridge, Alison M. An introduction to superprocesses. University Lecture Series, 20. American Mathematical Society, Providence, RI, 2000. xii+187 pp. ISBN: 0-8218-2706-5 MR1779100
•Falconer, K. J. The geometry of fractal sets. Cambridge Tracts in Mathematics, 85. Cambridge University Press, Cambridge, 1986. xiv+162 pp. ISBN: 0-521-25694-1; 0-521-33705-4 MR0867284
•Iscoe, I. On the supports of measure-valued critical branching Brownian motion. Ann. Probab. 16 (1988), no. 1, 200--221. MR0920265
•Mueller, Carl; Perkins, Edwin A. The compact support property for solutions to the heat equation with noise. Probab. Theory Related Fields 93 (1992), no. 3, 325--358. MR1180704
•Pitman, Jim. Coalescents with multiple collisions. Ann. Probab. 27 (1999), no. 4, 1870--1902. MR1742892
•Reimers, M. A new result on the support of the Fleming-Viot process, proved by nonstandard construction. Stochastics Stochastics Rep. 44 (1993), no. 3-4, 213--223. MR1277170
•Sagitov, Serik. The general coalescent with asynchronous mergers of ancestral lines. J. Appl. Probab. 36 (1999), no. 4, 1116--1125. MR1742154
•Schweinsberg, Jason. A necessary and sufficient condition for the $\Lambda$-coalescent to come down from infinity. Electron. Comm. Probab. 5 (2000), 1--11 (electronic). MR1736720
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