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

Princeton University Press
Free sample

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.

Read more

About the author

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.
Read more

Additional Information

Princeton University Press
Read more
Published on
Apr 4, 2013
Read more
Read more
Read more
Read more
Mathematics / Differential Equations / General
Mathematics / Probability & Statistics / Stochastic Processes
Science / Life Sciences / Biology
Read more
Content Protection
This content is DRM protected.
Read more
Read Aloud
Available on Android devices
Read more
Eligible for Family Library

Reading information

Smartphones and Tablets

Install the Google Play Books app for Android and iPad/iPhone. It syncs automatically with your account and allows you to read online or offline wherever you are.

Laptops and Computers

You can read books purchased on Google Play using your computer's web browser.

eReaders and other devices

To read on e-ink devices like the Sony eReader or Barnes & Noble Nook, you'll need to download a file and transfer it to your device. Please follow the detailed Help center instructions to transfer the files to supported eReaders.
With Wiley’s Enhanced E-Text, you get all the benefits of a downloadable, reflowable eBook with added resources to make your study time more effective, including:

• Embedded & searchable equations, figures & tables
• Math XML
• Index with linked pages numbers for easy reference
• Redrawn full color figures to allow for easier identification

Elementary Differential Equations and Boundary Value Problems 11e, like its predecessors, is written from the viewpoint of the applied mathematician, whose interest in differential equations may sometimes be quite theoretical, sometimes intensely practical, and often somewhere in between. The authors have sought to combine a sound and accurate (but not abstract) exposition of the elementary theory of differential equations with considerable material on methods of solution, analysis, and approximation that have proved useful in a wide variety of applications. While the general structure of the book remains unchanged, some notable changes have been made to improve the clarity and readability of basic material about differential equations and their applications. In addition to expanded explanations, the 11th edition includes new problems, updated figures and examples to help motivate students.

The program is primarily intended for undergraduate students of mathematics, science, or engineering, who typically take a course on differential equations during their first or second year of study. The main prerequisite for engaging with the program is a working knowledge of calculus, gained from a normal twoï¿1?2 or threeï¿1?2 semester course sequence or its equivalent. Some familiarity with matrices will also be helpful in the chapters on systems of differential equations.
©2018 GoogleSite Terms of ServicePrivacyDevelopersArtistsAbout Google
By purchasing this item, you are transacting with Google Payments and agreeing to the Google Payments Terms of Service and Privacy Notice.