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

By Matthias C. F. Birkner, Jochen Blath, Martin Moehle, Matthias Steinruecken, Johanna Tams. 2008

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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 a representation based on the empirical measure of an exchange- able particle system along the lines of Donnelly and Kurtz (1999). We establish pathwise convergence of the approximating systems to the limiting �-Fleming-Viot process with mutation. An alternative construction of the semigroup based on the

Subfields: Artificial Intelligence, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2468fd0ac44a17b8ecf776a03d451b40bf5bc304