Degenerate Diffusion Operators Arising in Population Biology PDF
By:Charles L. Epstein,Rafe Mazzeo
Published on 2013 by Princeton University Press
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 Holder 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. |
This Book was ranked at 14 by Google Books for keyword Science Math Nature Ecology novel.
Book ID of Degenerate Diffusion Operators Arising in Population Biology's Books is 0iJoZLBZXMcC, Book which was written byCharles L. Epstein,Rafe Mazzeohave ETAG "dy5meOVQ3Xk"
Book which was published by Princeton University Press since 2013 have ISBNs, ISBN 13 Code is 9780691157153 and ISBN 10 Code is 0691157154
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