Lookdown representation for tree-valued Fleming-Viot processes
Year: 2014
Type: preprint
Abstract: We construct the tree-valued Fleming-Viot process pathwise from the lookdown model. The tree-valued Fleming-Viot process was introduced by Greven, Pfaffelhuber, and Winter [Probab. Theory Related Fields (2013)], it has a.s. continuous paths. We generalize this process to include the cases with multiple reproduction events and simultaneous multiple reproduction events. In particular, we include the case with dust. We obtain a process with a.s. c\`adl\`ag paths and jumps at the times of large reproduction events. We state well-posed martingale problems. In case that the associated coalescent comes down from infinity, the construction from the lookdown model allows to read off a process with values in the space of measure-preserving isometry classes of compact metric measure spaces, endowed with the Gromov-Hausdorff-Prohorov metric. This process has a.s. c\`adl\`ag paths with additional jumps at the times when old families become extinct.
Source: arXiv (Cornell University)
Author: Stephan Gufler
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2240999265