Harnack Inequalities and Heat Kernel Estimates for Degenerate Diffusion Operators Arising in Population Biology
نویسندگان
چکیده
منابع مشابه
Harnack Inequalities and Heat-kernel Estimates for Degenerate Diffusion Operators Arising in Population Biology
This paper continues the analysis, started in [3, 4], of a class of degenerate elliptic operators defined on manifolds with corners, which arise in Population Biology. Using techniques pioneered by J. Moser, and extended and refined by L. Saloff-Coste, Grigor’yan, and Sturm, we show that weak solutions to the parabolic problem defined by a sub-class of these operators, which consists of those t...
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We analyze a class of partial differential equations that arise as"backwards Kolmogorov operators"in infinite population limits of the Wright-Fisher models in population genetics and in mathematical finance. These are degenerate elliptic operators defined on manifolds with corners. The classical example is the Kimura diffusion operator, which acts on functions defined on the simplex in R^n. We ...
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We study various probabilistic and analytical properties of a class of degenerate diffusion operators arising in Population Genetics, the so-called generalized Kimura diffusion operators [8, 9, 6]. Our main results are a stochastic representation of weak solutions to a degenerate parabolic equation with singular lower-order coefficients, and the proof of the scaleinvariant Harnack inequality fo...
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We prove the equivalence of parabolic Harnack inequalities and sub-Gaussian heat kernel estimates in a general metric measure space with a local regular Dirichlet form.
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We announce some results obtained in a recent study [14], concerning a general class of hypoelliptic evolution operators in R. A Gaussian lower bound for the fundamental solution and a global Harnack inequality are given.
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ژورنال
عنوان ژورنال: Applied Mathematics Research eXpress
سال: 2016
ISSN: 1687-1200,1687-1197
DOI: 10.1093/amrx/abw002