Degenerate Diffusion Operators Arising in Population Biology - Couverture souple

Epstein, Charles L.; Mazzeo, Rafe

 
9780691157153: Degenerate Diffusion Operators Arising in Population Biology
Couverture souple
ISBN 10 : 0691157154 ISBN 13 : 9780691157153
Editeur : Princeton University Press, 2013

Synopsis

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.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

À propos de l?auteur

Charles L. Epstein is the Thomas A. Scott Professor of Mathematics at the University of Pennsylvania. Rafe Mazzeo is professor of mathematics at Stanford University.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
Princeton University Press
Date d'édition
2013
Langue
anglais
ISBN 10 
0691157154
ISBN 13 
9780691157153
Reliure
Broché
Nombre de pages
320
Coordonnées du fabricant
Princeton University Press
https://press.princeton.edu/books

7th Floor, New South Building
PRINCETON
NJ
8544
Etats-Unis
Personne responsable
non disponible

Autres éditions populaires du même titre

9780691157122: Degenerate Diffusion Operators Arising in Population Biology

Edition présentée

ISBN 10 :  069115712X ISBN 13 :  9780691157122
Editeur : Princeton University Press, 2013
Couverture rigide