Change of measure in the lookdown particle system

We perform various changes of measure in the lookdown particle system of Donnelly and Kurtz. The first example is a product type h-transform related to conditioning a Generalized Fleming-Viot process without mutation on coexistence of some genetic types in remote time. We give a pathwise construction of this h-transform by just “forgetting” some reproduction events in the lookdown particle system. We also provide an intertwining relationship for the Wright-Fisher diffusion and explicit the associated pathwise decomposition. The second example, called the linear or additive h-transform, concerns a wider class of measure-valued processes with spatial motion. Applications include a simple description of the additiveh-transform of the Generalized Fleming-Viot process and an immortal particle representation for the additive h-transform of the Dawson-Watanabe process.