Degenerate Diffusion Operators Arising in Population Biology is popular PDF and ePub book, written by Charles L. Epstein in 2013-04-07, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Degenerate Diffusion Operators Arising in Population Biology can be Read Online from any device for your convenience.
Degenerate Diffusion Operators Arising in Population Biology Book PDF 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.
Detail Book of Degenerate Diffusion Operators Arising in Population Biology PDF
- Author : Charles L. Epstein
- Release : 07 April 2013
- Publisher : Princeton University Press
- ISBN : 9780691157153
- Genre : Mathematics
- Total Page : 320 pages
- Language : English
- PDF File Size : 7,9 Mb
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