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Degenerate Diffusion Operators Arising in Population Biology (AM-185) - Princeton Scholarship Online
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Degenerate Diffusion Operators Arising in Population Biology (AM-185)

Charles L. Epstein and Rafe Mazzeo


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. The book uses an “integral kernel method” to develop mathematical foundations for the study of such degenerate elliptic operators and the stochastic processes they define. The precise natur ... More

Keywords: manifold with corners, degenerate elliptic operator, population genetics, mathematical finance, martingale problem, heat equation, Hölder space, resolvent operator, forward Kolmogorov equation, backward Kolmogorov equation

Bibliographic Information

Print publication date: 2013 Print ISBN-13: 9780691157122
Published to Princeton Scholarship Online: October 2017 DOI:10.23943/princeton/9780691157122.001.0001


Affiliations are at time of print publication.

Charles L. Epstein, author
University of Pennsylvania

Rafe Mazzeo, author
Stanford University