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arXiv · 1508.03701

Diffusion on a Hypersphere: Application to the Wright-Fisher model

Kishiko Maruyama·Yoshiaki Itoh
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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.

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Kishiko Maruyama, Yoshiaki Itoh. 2015-08-15. Diffusion on a Hypersphere: Application to the Wright-Fisher model. https://arxiv.org/abs/1508.03701

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