• Corpus ID: 2169486

A modified lookdown construction for the Xi-Fleming-Viot process with mutation and populations with recurrent bottlenecks

  title={A modified lookdown construction for the Xi-Fleming-Viot process with mutation and populations with recurrent bottlenecks},
  author={Matthias C. F. Birkner and Jochen Blath and Martin Moehle and Matthias Steinruecken and Johanna Tams},
  journal={arXiv: Probability},
Letbe a finite measure on the unit interval. A �-Fleming-Viot process is a probability measure valued Markov process which is dual to a coalescent with multiple collisions (�-coalescent) in analogy to the duality known for the classical Fleming-Viot process and Kingman's coalescent, whereis the Dirac measure in 0. We explicitly construct a dual process of the coalescent with simultaneous multi- ple collisions (�-coalescent) with mutation, the �-Fleming-Viot process with muta- tion, and provide… 

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  • S. Sagitov
  • Mathematics
    Journal of Applied Probability
  • 1999
Take a sample of individuals in the fixed-size population model with exchangeable family sizes. Follow the ancestral lines for the sampled individuals backwards in time to observe the ancestral