Diffusion on a Hypersphere: Application to the Wright-Fisher model
Probability
2015-12-29 v2 Mathematical Physics
math.MP
Abstract
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.
Cite
@article{arxiv.1508.03701,
title = {Diffusion on a Hypersphere: Application to the Wright-Fisher model},
author = {Kishiko Maruyama and Yoshiaki Itoh},
journal= {arXiv preprint arXiv:1508.03701},
year = {2015}
}