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Degenerate diffusion operators arising in population biology [[electronic resource] /] / Charles L. Epstein and Rafe Mazzeo



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Autore: Epstein Charles L Visualizza persona
Titolo: Degenerate diffusion operators arising in population biology [[electronic resource] /] / Charles L. Epstein and Rafe Mazzeo Visualizza cluster
Pubblicazione: Princeton, : Princeton University Press, 2013
Edizione: Course Book
Descrizione fisica: 1 online resource (321 p.)
Disciplina: 577.8/801519233
Soggetto topico: Elliptic operators
Markov processes
Population biology - Mathematical models
Soggetto non controllato: 1-dimensional integral
Euclidean model problem
Euclidean space
Hlder space
Hopf boundary point
Kimura diffusion equation
Kimura diffusion operator
Laplace transform
Schauder estimate
WrightІisher geometry
adjoint operator
backward Kolmogorov equation
boundary behavior
degenerate elliptic operator
doubling
elliptic Kimura operator
elliptic equation
forward Kolmogorov equation
function space
general model problem
generalized Kimura diffusion
heat equation
heat kernel
higher dimensional corner
higher regularity
holomorphic semi-group
homogeneous Cauchy problem
hybrid space
hypersurface boundary
induction hypothesis
induction
inhomogeneous problem
irregular solution
long time asymptotics
long-time behavior
manifold with corners
martingale problem
mathematical finance
model problem
normal form
normal vector
null-space
off-diagonal behavior
open orthant
parabolic equation
perturbation theory
polyhedron
population genetics
probability theory
regularity
resolvent operator
semi-group
solution operator
uniqueness
Classificazione: SI 830
Altri autori: MazzeoRafe  
Note generali: Description based upon print version of record.
Nota di bibliografia: Includes bibliographical references and index.
Nota di contenuto: Front matter -- Contents -- Preface -- Chapter 1. Introduction -- Part I. Wright-Fisher Geometry and the Maximum Principle -- Chapter 2. Wright-Fisher Geometry -- Chapter 3. Maximum Principles and Uniqueness Theorems -- Part II. Analysis of Model Problems -- Chapter 4. The Model Solution Operators -- Chapter 5. Degenerate Hölder Spaces -- Chapter 6. Hölder Estimates for the 1-dimensional Model Problems -- Chapter 7. Hölder Estimates for Higher Dimensional Corner Models -- Chapter 8. Hölder Estimates for Euclidean Models -- Chapter 9. Hölder Estimates for General Models -- Part III. Analysis of Generalized Kimura Diffusions -- Chapter 10. Existence of Solutions -- Chapter 11. The Resolvent Operator -- Chapter 12. The Semi-group on ℂ°(P) -- Appendix A: Proofs of Estimates for the Degenerate 1-d Model -- Bibliography -- Index
Sommario/riassunto: 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 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.
Titolo autorizzato: Degenerate diffusion operators arising in population biology  Visualizza cluster
ISBN: 1-4008-4718-4
1-299-05145-6
1-4008-4610-2
Formato: Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione: Inglese
Record Nr.: 9910786024003321
Lo trovi qui: Univ. Federico II
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Serie: Annals of Mathematics Studies