2015/08/15 by Kishiko Maruyama, Yoshiaki Itoh, Maruyama, Kishiko +1
Mathematics · Physics and Astronomy · Biochemistry, Genetics and Molecular Biology · #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Diffusion and Search Dynamics
paper · pdf · doi:10.48550/arxiv.1508.03701
The eigenfunction expansion by Gegenbauer polynomials for the diffusion on a hypersphere is transformed into the diffusion for the Wright-Fisher model with a particular mutation rate. We use the Ito calculus considering stochastic differential equations. The expansion gives a simple interpretation of the Griffiths eigenfunction expansion for the Wright-Fisher model. Our representation is useful to simulate the Wright-Fisher model as well as Brownian motion on a hypersphere.