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Medientyp:
E-Artikel
Titel:
Quasistationary Distributions and Fleming-Viot Processes in Finite Spaces
Beteiligte:
Asselah, Amine;
Ferrari, Pablo A.;
Groisman, Pablo
Erschienen:
Cambridge University Press (CUP), 2011
Erschienen in:Journal of Applied Probability
Sprache:
Englisch
DOI:
10.1017/s0021900200007907
ISSN:
1475-6072;
0021-9002
Entstehung:
Anmerkungen:
Beschreibung:
<jats:p>Consider a continuous-time Markov process with transition rates matrix<jats:italic>Q</jats:italic>in the state space Λ ⋃ {0}. In the associated Fleming-Viot process<jats:italic>N</jats:italic>particles evolve independently in Λ with transition rates matrix<jats:italic>Q</jats:italic>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<jats:italic>N</jats:italic>→ ∞ 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<jats:italic>N</jats:italic>particles converges as<jats:italic>N</jats:italic>→ ∞ 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 /<jats:italic>N</jats:italic>.</jats:p>