Fleming-Viot selects the minimal quasi-stationary distribution: The Galton-Watson case
Consider N particles moving independently, each one according to a subcritical continuous-time Galton-Watson process unless it hits 0, at which time it jumps instantaneously to the position of one of the other particles chosen uniformly at random. The resulting dynamics is called Fleming-Viot proces...
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| Autores principales: | , , |
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2016
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02460203_v52_n2_p647_Asselah http://hdl.handle.net/20.500.12110/paper_02460203_v52_n2_p647_Asselah |
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| Sumario: | Consider N particles moving independently, each one according to a subcritical continuous-time Galton-Watson process unless it hits 0, at which time it jumps instantaneously to the position of one of the other particles chosen uniformly at random. The resulting dynamics is called Fleming-Viot process. We show that for each N there exists a unique invariant measure for the Fleming-Viot process, and that its stationary empirical distribution converges, as N goes to infinity, to the minimal quasi-stationary distribution of the Galton-Watson process conditioned on non-extinction. © Association des Publications de l'Institut Henri Poincaré, 2016. |
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