Artículo
Abstract:
Consider a continuous-time Markov process with transition rates matrix Q in the state space Λ ∪ {0}. In the associated Fleming-Viot process N particles evolve independently in Λ with transition rates matrix Q until one of them attempts to jump to state 0. At this moment the particle jumps to one of the positions of the other particles, chosen uniformly at random. When Λ is finite, we show that the empirical distribution of the particles at a fixed time converges as N → ∞ to the distribution of a single particle at the same time conditioned on not touching {0}. Furthermore, the empirical profile of the unique invariant measure for the Fleming-Viot process with N particles converges as N → ∞ to the unique quasistationary distribution of the one-particle motion. A key element of the approach is to show that the two-particle correlations are of order 1/N. © Applied Probability Trust 2011.
Registro:
| Documento: | Artículo |
| Título: | Quasistationary distributions and fleming-viot processes in finite spaces |
| Autor: | Asselah, A.; Ferrari, P.A.; Groisman, P. |
| Filiación: | LAMA, Université Paris-Est, CNRS UMR 8050, 61Avenue General de Gaulle, 94010 Creteil Cedex, France DM-FCEN, Universidad de Buenos Aires, Ciudad Universitaria, Pabellon 1, 1428 Buenos Aires, Argentina Universidade de São Paulo, Brazil Universidad de Buenos Aires, Argentina |
| Palabras clave: | Fleming-Viot process; Quasistationary distribution |
| Año: | 2011 |
| Volumen: | 48 |
| Número: | 2 |
| Página de inicio: | 322 |
| Página de fin: | 332 |
| DOI: | http://dx.doi.org/10.1239/jap/1308662630 |
| Título revista: | Journal of Applied Probability |
| Título revista abreviado: | J. Appl. Probab. |
| ISSN: | 00219002 |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00219002_v48_n2_p322_Asselah |
Referencias:
- Bieniek, M., Burdzy, K., Finch, S., (2009) Non-extinction of A Fleming-Viot Particle Model., , http://arxiv.org/abs/0905.1999v1, Preprint. Available at
- Burdzy, K., Hołyst, R., March, P., A fleming-viot particle representation of the dirichlet laplacian (2000) Commun. Math. Phys., 214, pp. 679-703
- Darroch, J.N., Seneta, E., On quasi-stationary distributions in absorbing continuous-time finite Markov chains (1967) J. Appl. Prob., 4, pp. 192-196
- Ferrari, P.A., Maríc, N., Quasi stationary distributions and Fleming-Viot processes in countable spaces (2007) Electron. J. Prob., 12, pp. 684-702
- Grigorescu, I., Kang, M., Hydrodynamic limit for a Fleming-Viot type system (2004) Stochastic Processes and their Applications, 110 (1), pp. 111-143. , DOI 10.1016/j.spa.2003.10.010, PII S0304414903001716
- Grigorescu, I., Kang, M., Tagged particle limit for a Fleming-Viot type system (2006) Electronic Journal of Probability, 11, pp. 311-331. , http://www.math.washington.edu/~ejpecp/include/getdoc.php?id= 3527&article=1578&mode=pdf
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Citas:
---------- APA ----------
Asselah, A., Ferrari, P.A. & Groisman, P. (2011) . Quasistationary distributions and fleming-viot processes in finite spaces. Journal of Applied Probability, 48(2), 322-332.http://dx.doi.org/10.1239/jap/1308662630
---------- CHICAGO ----------
Asselah, A., Ferrari, P.A., Groisman, P. "Quasistationary distributions and fleming-viot processes in finite spaces" . Journal of Applied Probability 48, no. 2 (2011) : 322-332.http://dx.doi.org/10.1239/jap/1308662630
---------- MLA ----------
Asselah, A., Ferrari, P.A., Groisman, P. "Quasistationary distributions and fleming-viot processes in finite spaces" . Journal of Applied Probability, vol. 48, no. 2, 2011, pp. 322-332.http://dx.doi.org/10.1239/jap/1308662630
---------- VANCOUVER ----------
Asselah, A., Ferrari, P.A., Groisman, P. Quasistationary distributions and fleming-viot processes in finite spaces. J. Appl. Probab. 2011;48(2):322-332.http://dx.doi.org/10.1239/jap/1308662630
