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

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
Creator
Contributor
Subject
Genre
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 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."--Publisher's website
Member of
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
Instantiates
Publication
Bibliography note
Includes bibliographical references and index
Contents
Introduction. Part 1: Wright-Fisher geometry and the maximum principle. Wright-Fisher geometry ; Maximum principles and uniqueness theorems. -- Part 2: Analysis of model problems. The model solution operators ; Degenerate Hölder spaces ; Hölder estimates for the 1-dimensional 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 semi-group 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
Publication
Bibliography note
Includes bibliographical references and index
Contents
Introduction. Part 1: Wright-Fisher geometry and the maximum principle. Wright-Fisher geometry ; Maximum principles and uniqueness theorems. -- Part 2: Analysis of model problems. The model solution operators ; Degenerate Hölder spaces ; Hölder estimates for the 1-dimensional 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 semi-group 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

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