On the weak convergence of Wright-Fisher model

Harry A. Guess

Stochastic Processes and their Applications, 1973, vol. 1, issue 3, 287-306

Abstract: We prove that the sequence of stochastic processes obtained from Wright-Fisher models by transforming the time scales and state spaces in the usual way converges weakly to a diffusion process on the time interval [0,[infinity]). Convergence of fixation probabilities and fixation time distributions are obtained as corollaries. These results extend a theorem of Watterson, who proved convergence in distribution to a diffusion at any given single time point for these processes.

Date: 1973
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