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Wednesday, February 21, 2024 - 14:15 in T2-149


Simplified Wright-Fisher processes and non-linear extensions

A talk in the Other series by
Leonardo Videla from Universidad de Santiago de Chile

Abstract: In this talk I will present some results regarding a family of Markov kernels on the unit interval which, after rescaling, are proved to converge in law to diffusion processes of the Wright-Fisher type. Discrete-time line-counting processes (the ancestral lineage processes) are obtained, and we prove that moment duality relations hold for a large class of variants of the basic process. This unified, parsimonious derivation of some well-known population genetic processes allows one to easily extend the dynamics to the case where mutations and/or selection rates might depend on the instantaneous distribution of the process. In this connection we prove both, propagation of chaos for the associated particle system in mean-field regime, and the convergence of the rescaled discrete-time non-linear Wright-Fisher conglomerate to diffusions of the McKean-Vlasov type. As an important intermediate step, it is proved that the sequence of (laws of) some non-linear Markov chains converge to the unique solution of a non-linear martingale problem.

Within the CRC this talk is associated to the project(s): C1



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