Analysis and geometry of Markov diffusion operators [electronic resource] / Dominique Bakry, Ivan Gentil, Michel Ledoux.
Bakry, D. (Dominique), author.; Gentil, Ivan, author.; Ledoux, Michel, 1958-, author.
2014
QA274.7
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Title Analysis and geometry of Markov diffusion operators [electronic resource] / Dominique Bakry, Ivan Gentil, Michel Ledoux.
Author Bakry, D. (Dominique), author.
ISBN 9783319002279 electronic book
3319002279 electronic book
9783319002262
DOI https://doi.org/10.1007/978-3-319-00227-9
Published Cham : Springer, 2014.
Language English
Description 1 online resource (xx, 552 pages).
Other Standard Identifiers 10.1007/978-3-319-00227-9 doi
Call Number QA274.7
Dewey Decimal Classification 519.2/33
Summary The present volume is an extensive monograph on the analytic and geometric aspects of Markov diffusion operators. It focuses on the geometric curvature properties of the underlying structure in order to study convergence to equilibrium, spectral bounds, functional inequalities such as Poincar, Sobolev or logarithmic Sobolev inequalities, and various bounds on solutions of evolution equations. At the same time, it covers a large class of evolution and partial differential equations. The book is intended to serve as an introduction to the subject and to be accessible for beginning and advanced scientists and non-specialists. Simultaneously, it covers a wide range of results and techniques from the early developments in the mid-eighties to the latest achievements. As such, students and researchers interested in the modern aspects of Markov diffusion operators and semigroups and their connections to analytic functional inequalities, probabilistic convergence to equilibrium and geometric curvature will find it especially useful. Selected chapters can also be used for advanced courses on the topic.
Bibliography, etc. Note Includes bibliographical references and index.
Access Note Access limited to authorized users.
Source of Description Description based on print version record.
Added Author Gentil, Ivan, author.
Ledoux, Michel, 1958-, author.
Series Grundlehren der mathematischen Wissenschaften ; 348.
Available in Other Form Analysis and geometry of Markov diffusion operators
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Introduction
Part I Markov semigroups, basics and examples: 1.Markov semigroups
2.Model examples
3.General setting
Part II Three model functional inequalities: 4.Poincar inequalities
5.Logarithmic Sobolev inequalities
6.Sobolev inequalities
Part III Related functional, isoperimetric and transportation inequalities: 7.Generalized functional inequalities
8.Capacity and isoperimetry-type inequalities
9.Optimal transportation and functional inequalities
Part IV Appendices: A.Semigroups of bounded operators on a Banach space
B.Elements of stochastic calculus
C.Some basic notions in differential and Riemannian geometry
Notations and list of symbols.

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