Convergence of One-Dimensional Diffusion Processes to a Jump Process Related to Population Genetics
NORTH CAROLINA UNIV AT CHAPEL HILL CENTER FOR STOCHASTIC PROCESSES
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A conjecture on the convergence of diffusion models in population genetics to a simple Markov chain model is proved. The notion of bi-generalized diffusion processes and their limit theorems are used systematically to prove the conjecture. Three limits strong selection--weak mutation limit, moderate selection--weak mutation limit, weak selection--weak mutation limit are considered for typical diffusion models in population genetics.