Analysis and Geometry of Markov Diffusion Operators
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, Sobo...
| Main Authors: | , , |
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| Corporate Author: | |
| Language: | English |
| Published: |
Cham :
Springer International Publishing : Imprint: Springer,
2014.
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| Edition: | 1st ed. 2014. |
| Series: | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics,
348 |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/978-3-319-00227-9 |
Table of Contents:
- 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.