This 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.
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