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Analysis and Geometry of Markov Diffusion Operators
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Catalogue Information
Field name
Details
Dewey Class
515 (DDC 23)
Title
Analysis and Geometry of Markov Diffusion Operators (EB) / by Dominique Bakry, Ivan Gentil, Michel Ledoux.
Author
Bakry, Dominique
Added Personal Name
Gentil, Ivan
author.
Ledoux, Michel
author.
Other name(s)
SpringerLink (Online service)
Publication
Cham : : Springer International Publishing, , 2014.
Physical Details
XX, 552 p. : online resource.
ISBN
9783319002279
Summary Note
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 Poincaré, 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.:
Contents note
Introduction -- Part I Markov semigroups, basics and examples: 1.Markov semigroups -- 2.Model examples -- 3.General setting -- Part II Three model functional inequalities: 4.Poincaré 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 -- Bibliography -- Index.
System details note
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site
http://dx.doi.org/10.1007/978-3-319-00227-9
Links to Related Works
Subject References:
Analysis
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Differential equations, Partial
.
Differential Geometry
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Distribution (Probability theory)
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Functional Analysis
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Global analysis (Mathematics)
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Global differential geometry
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Partial differential equations
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Probability theory and stochastic processes
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Authors:
Bakry, Dominique
.
Gentil, Ivan
.
Ledoux, Michel
.
Corporate Authors:
SpringerLink (Online service)
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Series:
Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics
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Classification:
515 (DDC 23)
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