Mathematical Sciences: Some Aspects of Markov Processes in Population Genetics

点击翻译按钮获取中文摘要

This research will study stochastic models in mathematical population genetics. The first set of problems concerns measure- valued diffusion processes that generalize the usual K-allele diffusion model of population genetics. The investigator will study the ergodicity of the selective infinitely-many-alleles model, properties of the two-locus model, and existence of the infinitely-many-sites model with recombination. The second set of problems relates to Gaussian diffusion approximations of genetic models with two time scales, and convergence of an ancestral Markov chain related to the coalescent.