Ranked masses in two-parameter Fleming–Viot diffusions

In previous work, we constructed Fleming–Viot-type measure-valued diffusions (and diffusions on a space of interval partitions of the unit interval [0,1]) that are stationary with the Poisson–Dirichlet laws with parameters α ∈ (0,1) and θ ≥ 0. In this paper, we complete the proof that these processes resolve a conjecture by Feng and Sun (2010) by showing that the processes of ranked atom sizes (or of ranked interval lengths) of these diffusions are members of a two-parameter family of diffusions introduced by Petrov (2009), extending a model by Ethier and Kurtz (1981) in the case α= 0. The latter diffusions are continuum limits of up-down Chinese restaurant processes.

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