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The Resource Degenerate diffusion operators arising in population biology, Charles L. Epstein and Rafe Mazzeo
Degenerate diffusion operators arising in population biology, Charles L. Epstein and Rafe Mazzeo
Resource Information
The item Degenerate diffusion operators arising in population biology, Charles L. Epstein and Rafe Mazzeo represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.This item is available to borrow from all library branches.
Resource Information
The item Degenerate diffusion operators arising in population biology, Charles L. Epstein and Rafe Mazzeo represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.
This item is available to borrow from all library branches.
 Summary
 "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 halfplane. Epstein and Mazzeo also demonstrate precise asymptotic results for the longtime behavior of solutions to both the forward and backward Kolmogorov equations."Publisher's website
 Language
 eng
 Extent
 1 online resource (pages cm.)
 Contents

 Introduction. Part 1: WrightFisher geometry and the maximum principle. WrightFisher geometry ; Maximum principles and uniqueness theorems.
 Part 2: Analysis of model problems. The model solution operators ; Degenerate Hölder spaces ; Hölder estimates for the 1dimensional model problems ; Hölder estimates for higher dimensional corner models ; Hölder estimates for Euclidean models ; Hölder estimates for general models.
 Part 3: Analysis of generalized Kimura diffusions. Existence of solutions ; The resolvent operator ; The semigroup on l0(P)
 Isbn
 9781400846108
 Label
 Degenerate diffusion operators arising in population biology
 Title
 Degenerate diffusion operators arising in population biology
 Statement of responsibility
 Charles L. Epstein and Rafe Mazzeo
 Subject

 Elliptic operators
 Elliptic operators
 MATHEMATICS / Differential Equations / General
 Markov processes
 Markov processes
 Markov processes
 Markov processes
 NATURE / Ecology
 NATURE / Ecosystems & Habitats / Wilderness
 Population biology  Mathematical models
 Population biology  Mathematical models
 Population biology  Mathematical models
 Population biology  Mathematical models
 SCIENCE / Environmental Science
 SCIENCE / Life Sciences / Ecology
 Electronic books
 Elliptic operators
 Elliptic operators
 Language
 eng
 Summary
 "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 halfplane. Epstein and Mazzeo also demonstrate precise asymptotic results for the longtime behavior of solutions to both the forward and backward Kolmogorov equations."Publisher's website
 Cataloging source
 YDXCP
 http://library.link/vocab/creatorName
 Epstein, Charles L
 Index
 index present
 LC call number
 QA329.42
 LC item number
 .E67 2013
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 http://library.link/vocab/relatedWorkOrContributorName
 Mazzeo, Rafe
 Series statement
 Annals of mathematics studies
 Series volume
 no. 185
 http://library.link/vocab/subjectName

 Elliptic operators
 Markov processes
 Population biology
 NATURE / Ecology
 NATURE / Ecosystems & Habitats / Wilderness
 SCIENCE / Environmental Science
 SCIENCE / Life Sciences / Ecology
 MATHEMATICS / Differential Equations / General
 Elliptic operators
 Markov processes
 Population biology
 Label
 Degenerate diffusion operators arising in population biology, Charles L. Epstein and Rafe Mazzeo
 Bibliography note
 Includes bibliographical references and index
 Contents
 Introduction. Part 1: WrightFisher geometry and the maximum principle. WrightFisher geometry ; Maximum principles and uniqueness theorems.  Part 2: Analysis of model problems. The model solution operators ; Degenerate Hölder spaces ; Hölder estimates for the 1dimensional model problems ; Hölder estimates for higher dimensional corner models ; Hölder estimates for Euclidean models ; Hölder estimates for general models.  Part 3: Analysis of generalized Kimura diffusions. Existence of solutions ; The resolvent operator ; The semigroup on l0(P)
 Dimensions
 unknown
 Extent
 1 online resource (pages cm.)
 Form of item
 online
 Isbn
 9781400846108
 Isbn Type
 (electronic bk.)
 Specific material designation
 remote
 Stock number
 22573/ctt212gzm
 System control number

 (OCoLC)824353625
 (OCoLC)ocn824353625
 Label
 Degenerate diffusion operators arising in population biology, Charles L. Epstein and Rafe Mazzeo
 Bibliography note
 Includes bibliographical references and index
 Contents
 Introduction. Part 1: WrightFisher geometry and the maximum principle. WrightFisher geometry ; Maximum principles and uniqueness theorems.  Part 2: Analysis of model problems. The model solution operators ; Degenerate Hölder spaces ; Hölder estimates for the 1dimensional model problems ; Hölder estimates for higher dimensional corner models ; Hölder estimates for Euclidean models ; Hölder estimates for general models.  Part 3: Analysis of generalized Kimura diffusions. Existence of solutions ; The resolvent operator ; The semigroup on l0(P)
 Dimensions
 unknown
 Extent
 1 online resource (pages cm.)
 Form of item
 online
 Isbn
 9781400846108
 Isbn Type
 (electronic bk.)
 Specific material designation
 remote
 Stock number
 22573/ctt212gzm
 System control number

 (OCoLC)824353625
 (OCoLC)ocn824353625
Subject
 Elliptic operators
 Elliptic operators
 MATHEMATICS / Differential Equations / General
 Markov processes
 Markov processes
 Markov processes
 Markov processes
 NATURE / Ecology
 NATURE / Ecosystems & Habitats / Wilderness
 Population biology  Mathematical models
 Population biology  Mathematical models
 Population biology  Mathematical models
 Population biology  Mathematical models
 SCIENCE / Environmental Science
 SCIENCE / Life Sciences / Ecology
 Electronic books
 Elliptic operators
 Elliptic operators
Genre
Member of
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.bu.edu/portal/Degeneratediffusionoperatorsarisingin/oDRWZrzzwO8/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.bu.edu/portal/Degeneratediffusionoperatorsarisingin/oDRWZrzzwO8/">Degenerate diffusion operators arising in population biology, Charles L. Epstein and Rafe Mazzeo</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.bu.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.bu.edu/">Boston University Libraries</a></span></span></span></span></div>