LEADER 04550nam 2200733Ia 450 001 9910463088903321 005 20210514021227.0 010 $a1-4008-4718-4 010 $a1-299-05145-6 010 $a1-4008-4610-2 024 7 $a10.1515/9781400846108 035 $a(CKB)2670000000329084 035 $a(EBL)1108463 035 $a(OCoLC)824353625 035 $a(SSID)ssj0000819655 035 $a(PQKBManifestationID)11482109 035 $a(PQKBTitleCode)TC0000819655 035 $a(PQKBWorkID)10844911 035 $a(PQKB)10202368 035 $a(MiAaPQ)EBC1108463 035 $a(StDuBDS)EDZ0000515171 035 $a(DE-B1597)447147 035 $a(OCoLC)979686038 035 $a(DE-B1597)9781400846108 035 $a(Au-PeEL)EBL1108463 035 $a(CaPaEBR)ebr10643943 035 $a(CaONFJC)MIL436395 035 $a(EXLCZ)992670000000329084 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 608 $aElectronic books. 615 0$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 $a9910463088903321 996 $aDegenerate diffusion operators arising in population biology$9833201 997 $aUNINA