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035   $a(OCoLC)824353625
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035   $a(DE-B1597)9781400846108
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100   $a20120730d2013      uy             0
101 0 $aeng
135   $aurun#---|u||u
181   $ctxt
182   $cc
183   $acr
200 10$aDegenerate diffusion operators arising in population biology$b[electronic resource] /$fCharles L. Epstein and Rafe Mazzeo
205   $aCourse Book
210   $aPrinceton $cPrinceton University Press$d2013
215   $a1 online resource (321 p.)
225 0 $aAnnals of mathematics studies ;$vnumber 185
300   $aDescription based upon print version of record.
311 0 $a0-691-15712-X 
311 0 $a0-691-15715-4 
320   $aIncludes bibliographical references and index.
327   $tFront matter --$tContents --$tPreface --$tChapter 1. Introduction --$tPart I. Wright-Fisher Geometry and the Maximum Principle --$tChapter 2. Wright-Fisher Geometry --$tChapter 3. Maximum Principles and Uniqueness Theorems --$tPart II. Analysis of Model Problems --$tChapter 4. The Model Solution Operators --$tChapter 5. Degenerate Hölder Spaces --$tChapter 6. Hölder Estimates for the 1-dimensional Model Problems --$tChapter 7. Hölder Estimates for Higher Dimensional Corner Models --$tChapter 8. Hölder Estimates for Euclidean Models --$tChapter 9. Hölder Estimates for General Models --$tPart III. Analysis of Generalized Kimura Diffusions --$tChapter 10. Existence of Solutions --$tChapter 11. The Resolvent Operator --$tChapter 12. The Semi-group on ?°(P) --$tAppendix A: Proofs of Estimates for the Degenerate 1-d Model --$tBibliography --$tIndex
330   $aThis book provides the mathematical foundations for the analysis of a class of degenerate elliptic operators defined on manifolds with corners, which arise in a variety of applications such as population genetics, mathematical finance, and economics. The results discussed in this book prove the uniqueness of the solution to the Martingale problem and therefore the existence of the associated Markov process. Charles Epstein and Rafe Mazzeo use an "integral kernel method" to develop mathematical foundations for the study of such degenerate elliptic operators and the stochastic processes they define. The precise nature of the degeneracies of the principal symbol for these operators leads to solutions of the parabolic and elliptic problems that display novel regularity properties. Dually, the adjoint operator allows for rather dramatic singularities, such as measures supported on high co-dimensional strata of the boundary. Epstein and Mazzeo establish the uniqueness, existence, and sharp regularity properties for solutions to the homogeneous and inhomogeneous heat equations, as well as a complete analysis of the resolvent operator acting on Hölder spaces. They show that the semigroups defined by these operators have holomorphic extensions to the right half-plane. Epstein and Mazzeo also demonstrate precise asymptotic results for the long-time behavior of solutions to both the forward and backward Kolmogorov equations.
410  0$aAnnals of Mathematics Studies
606   $aElliptic operators
606   $aMarkov processes
606   $aPopulation biology$xMathematical models
610   $a1-dimensional integral.
610   $aEuclidean model problem.
610   $aEuclidean space.
610   $aHlder space.
610   $aHopf boundary point.
610   $aKimura diffusion equation.
610   $aKimura diffusion operator.
610   $aLaplace transform.
610   $aSchauder estimate.
610   $aWright?isher geometry.
610   $aadjoint operator.
610   $abackward Kolmogorov equation.
610   $aboundary behavior.
610   $adegenerate elliptic operator.
610   $adoubling.
610   $aelliptic Kimura operator.
610   $aelliptic equation.
610   $aforward Kolmogorov equation.
610   $afunction space.
610   $ageneral model problem.
610   $ageneralized Kimura diffusion.
610   $aheat equation.
610   $aheat kernel.
610   $ahigher dimensional corner.
610   $ahigher regularity.
610   $aholomorphic semi-group.
610   $ahomogeneous Cauchy problem.
610   $ahybrid space.
610   $ahypersurface boundary.
610   $ainduction hypothesis.
610   $ainduction.
610   $ainhomogeneous problem.
610   $airregular solution.
610   $along time asymptotics.
610   $along-time behavior.
610   $amanifold with corners.
610   $amartingale problem.
610   $amathematical finance.
610   $amodel problem.
610   $anormal form.
610   $anormal vector.
610   $anull-space.
610   $aoff-diagonal behavior.
610   $aopen orthant.
610   $aparabolic equation.
610   $aperturbation theory.
610   $apolyhedron.
610   $apopulation genetics.
610   $aprobability theory.
610   $aregularity.
610   $aresolvent operator.
610   $asemi-group.
610   $asolution operator.
610   $auniqueness.
615  0$aElliptic operators.
615  0$aMarkov processes.
615  0$aPopulation biology$xMathematical models.
676   $a577.8/801519233
686   $aSI 830$2rvk
700   $aEpstein$b Charles L$094497
701   $aMazzeo$b Rafe$0521267
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910786024003321
996   $aDegenerate diffusion operators arising in population biology$9833201
997   $aUNINA