Analysis and Geometry of Markov Diffusion Operators/
Bakry, Dominique
Analysis and Geometry of Markov Diffusion Operators/ Dominique Bakry ;Ivan Gentil ; Michel Ledoux - Switzerland: Springer International Publishing, 2014. - Grundlehren der mathematischen Wissenschaften 348 .
A Series of Comprehensive Studies in Mathematics
Markov Semigroups, Basic and Examples
Three Model Functional Inequalities
Related Functional, Isoperimetric and Transportation Inequalities
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 andgeometric curvature will find it especially useful. Selected chapters can also be used for advanced courses on the topic.
9783319002262
Markov Diffusion Operators
Analysis and Geometry of Markov Diffusion Operators/ Dominique Bakry ;Ivan Gentil ; Michel Ledoux - Switzerland: Springer International Publishing, 2014. - Grundlehren der mathematischen Wissenschaften 348 .
A Series of Comprehensive Studies in Mathematics
Markov Semigroups, Basic and Examples
Three Model Functional Inequalities
Related Functional, Isoperimetric and Transportation Inequalities
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 andgeometric curvature will find it especially useful. Selected chapters can also be used for advanced courses on the topic.
9783319002262
Markov Diffusion Operators