We identify stationary distributions of generalized Fleming–Viot processes with jump mechanisms specified by certain beta laws together with a parameter measure. Each of these distributions is obtained from normalized stable random measures after a suitable biased transformation followed by mixing by the law of a Dirichlet random measure with the same parameter measure. The calculations are based primarily on the well-known relationship to measure-valued branching processes with immigration.
"Stationary distributions for a class of generalized Fleming–Viot processes." Ann. Probab. 42 (3) 1257 - 1284, May 2014. https://doi.org/10.1214/12-AOP829