Wright–Fisher Diffusion in One Dimension

We analyze the diffusion processes associated to equations of Wright-Fisher type in one spatial dimension. These are associated to the degenerate heat equation ... on the interval $[0,1], where a(x)>0 on the interior and vanishes simply at the end points and ... is a vector field which is inward...

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Bibliographic Details
Published in:SIAM journal on mathematical analysis 2010-01, Vol.42 (2), p.568-608
Main Authors: Epstein, Charles L, Mazzeo, Rafe
Format: Article
Language:English
Subjects:
Asymptotic properties
Biology
Diffusion
Flux
Genetic algorithms
Heat equations
Mathematical analysis
Partial differential equations
Regularity
Studies
Vectors (mathematics)
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Summary:We analyze the diffusion processes associated to equations of Wright-Fisher type in one spatial dimension. These are associated to the degenerate heat equation ... on the interval $[0,1], where a(x)>0 on the interior and vanishes simply at the end points and ... is a vector field which is inward pointing at both ends. We consider various aspects of this problem, motivated by their applications in biology, including a sharp regularity theory for the "zero flux" boundary conditions, as well as an analysis of the infinitesimal generators of the C^sup m^-semigroups and their adjoints. Using these results we obtain precise asymptotics of solutions of this equation, both as t [arrow right] 0,∞ and as x [arrow right] 0,1.(ProQuest: ... denotes formulae omitted.)
ISSN:0036-1410
1095-7154
DOI:10.1137/090766152