Wright-Fisher Diffusion in One Dimension

Details Wright-Fisher Diffusion in One Dimension Wright-Fisher Diffusion in One Dimension

2009-07-22

arxiv.org/abs/0907.3881v1

Mathematics

Analysis of PDEs

55 pages

Scientific paper

We analyze the diffusion processes associated to equations of Wright-Fisher type in one spatial dimension. These are defined by a degenerate second order operator on the interval [0, 1], where the coefficient of the second order term vanishes simply at the endpoints, and the first order term is an inward-pointing vector field. We consider various aspects of this problem, motivated by applications in population genetics, including a sharp regularity theory for the zero flux boundary conditions, as well as a derivation of the precise asymptotics for solutions of this equation, both as t goes to 0 and infinity, and as x goes to 0, 1.

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