Change of measure in the lookdown particle system
(2012)cite arxiv:1204.0540.Abstract
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 additive h-transform of the Generalized Fleming Viot
process, which confirms a suggestion of Overbeck for the usual Fleming Viot
process -an immortal particle representation for the additive h-transform of
the Dawson Watanabe process.