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Transition Probabilities for Degenerate Diffusions Arising in Population Genetics

Thursday, March 31, 2016 - 11:00am - 12:00pm
Lind 305
Camelia Pop (University of Minnesota, Twin Cities)
We study the transition probabilities of a class of degenerate diffusions arising as models for gene frequencies in population genetics. The processes we consider are a generalization of the classical Wright-Fisher model, and they are defined through their infinitesimal generator, which is a boundary-degenerate operator defined on compact manifolds with corners, of which simplices and convex polyhedra are particular examples. Under suitable conditions, we find that the transition probabilities have a singular structure that described the absorbing and reflecting behavior of the underlying diffusion on the boundary components of the compact manifold with corners. This is joint work with Charles Epstein.
MSC Code: 
92Dxx