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Article Dans Une Revue Journal of Applied Probability Année : 2011

QUASISTATIONARY DISTRIBUTIONS AND FLEMING-VIOT PROCESSES IN FINITE SPACES

Résumé

Consider a continuous-time Markov process with transition rates matrix Q in the state space Lambda boolean OR {0}. In In the associated Fleming-Viot process N particles evolve independently in A 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 Lambda is finite, we show that the empirical distribution of the particles at a fixed time converges as N -> infinity 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 -> infinity 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.

Dates et versions

hal-00692986 , version 1 (01-05-2012)

Identifiants

Citer

Amine Asselah, Pablo A. Ferrari, Pablo Groisman. QUASISTATIONARY DISTRIBUTIONS AND FLEMING-VIOT PROCESSES IN FINITE SPACES. Journal of Applied Probability, 2011, 48 (2), pp.322. ⟨10.1239/jap/1308662630⟩. ⟨hal-00692986⟩
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