2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/124831This paper provides a construction of a Fleming--Viot measure valued diffusion process, for which the transition function is known, by extending recent ideas of the Gibbs sampler based Markov processes. In particular, we concentrate on the Chapman--Kolmogorov consistency conditions which allows a simple derivation of such a Fleming--Viot process, once a key and apparently new combinatorial result for Pólya-urn sequences has been established.Published at http://dx.doi.org/10.1214/105051606000000600 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)Probability60G57, 60J35 (Primary) 60J60, 92D15 (Secondary)text