Degenerate dffusion operators arising in population biology:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Princeton, N.J.
Princeton University Press
[2013]
|
| Schriftenreihe: | Annals of Mathematics Studies
number 185 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This 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 codimensional 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 |
| Beschreibung: | 1 Online-Ressource (320p.) |
| ISBN: | 9781400846108 |
| DOI: | 10.1515/9781400846108 |
Internformat
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| 490 | 1 | |a Annals of Mathematics Studies |v number 185 | |
| 500 | |a This 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 codimensional 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 | ||
| 546 | |a In English | ||
| 650 | 4 | |a Biowissenschaften, Biologie | |
| 650 | 4 | |a Elliptic operators | |
| 650 | 4 | |a Markov processes | |
| 650 | 4 | |a Population biology / Mathematical models | |
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| 650 | 7 | |a SCIENCE / Life Sciences / Ecology |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS / Differential Equations / General |2 bisacsh | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Ökologie | |
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Datensatz im Suchindex
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| author | Epstein, Charles L. 1957- Mazzeo, Rafe 1961- |
| author_GND | (DE-588)133727807 (DE-588)1035781999 |
| author_facet | Epstein, Charles L. 1957- Mazzeo, Rafe 1961- |
| author_role | aut aut |
| author_sort | Epstein, Charles L. 1957- |
| author_variant | c l e cl cle r m rm |
| building | Verbundindex |
| bvnumber | BV042523088 |
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| collection | ZDB-23-DGG ZDB-23-PST |
| ctrlnum | (OCoLC)824353625 (DE-599)BVBBV042523088 |
| dewey-full | 577.8/801519233 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 577 - Ecology |
| dewey-raw | 577.8/801519233 |
| dewey-search | 577.8/801519233 |
| dewey-sort | 3577.8 9801519233 |
| dewey-tens | 570 - Biology |
| discipline | Biologie Mathematik |
| doi_str_mv | 10.1515/9781400846108 |
| format | Electronic eBook |
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| id | DE-604.BV042523088 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:24:02Z |
| institution | BVB |
| isbn | 9781400846108 |
| language | English |
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| spelling | Epstein, Charles L. 1957- (DE-588)133727807 aut Degenerate dffusion operators arising in population biology Charles L. Epstein and Rafe Mazzeo Princeton, N.J. Princeton University Press [2013] © 2013 1 Online-Ressource (320p.) txt rdacontent c rdamedia cr rdacarrier Annals of Mathematics Studies number 185 This 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 codimensional 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 In English Biowissenschaften, Biologie Elliptic operators Markov processes Population biology / Mathematical models NATURE / Ecology bisacsh NATURE / Ecosystems & Habitats / Wilderness bisacsh SCIENCE / Environmental Science bisacsh SCIENCE / Life Sciences / Ecology bisacsh MATHEMATICS / Differential Equations / General bisacsh Mathematisches Modell Ökologie Mazzeo, Rafe 1961- (DE-588)1035781999 aut Erscheint auch als Druck-Ausgabe 978-0-691-15712-2 Annals of Mathematics Studies number 185 (DE-604)BV040389493 185 https://doi.org/10.1515/9781400846108?locatt=mode:legacy Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Epstein, Charles L. 1957- Mazzeo, Rafe 1961- Degenerate dffusion operators arising in population biology Annals of Mathematics Studies Biowissenschaften, Biologie Elliptic operators Markov processes Population biology / Mathematical models NATURE / Ecology bisacsh NATURE / Ecosystems & Habitats / Wilderness bisacsh SCIENCE / Environmental Science bisacsh SCIENCE / Life Sciences / Ecology bisacsh MATHEMATICS / Differential Equations / General bisacsh Mathematisches Modell Ökologie |
| title | Degenerate dffusion operators arising in population biology |
| title_auth | Degenerate dffusion operators arising in population biology |
| title_exact_search | Degenerate dffusion operators arising in population biology |
| title_full | Degenerate dffusion operators arising in population biology Charles L. Epstein and Rafe Mazzeo |
| title_fullStr | Degenerate dffusion operators arising in population biology Charles L. Epstein and Rafe Mazzeo |
| title_full_unstemmed | Degenerate dffusion operators arising in population biology Charles L. Epstein and Rafe Mazzeo |
| title_short | Degenerate dffusion operators arising in population biology |
| title_sort | degenerate dffusion operators arising in population biology |
| topic | Biowissenschaften, Biologie Elliptic operators Markov processes Population biology / Mathematical models NATURE / Ecology bisacsh NATURE / Ecosystems & Habitats / Wilderness bisacsh SCIENCE / Environmental Science bisacsh SCIENCE / Life Sciences / Ecology bisacsh MATHEMATICS / Differential Equations / General bisacsh Mathematisches Modell Ökologie |
| topic_facet | Biowissenschaften, Biologie Elliptic operators Markov processes Population biology / Mathematical models NATURE / Ecology NATURE / Ecosystems & Habitats / Wilderness SCIENCE / Environmental Science SCIENCE / Life Sciences / Ecology MATHEMATICS / Differential Equations / General Mathematisches Modell Ökologie |
| url | https://doi.org/10.1515/9781400846108?locatt=mode:legacy |
| volume_link | (DE-604)BV040389493 |
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