Analysis and geometry of Markov diffusion operators

Author(s)

• Bakry, D. (Dominique)
• Gentil, Ivan
• Ledoux, Michel

Bibliographic Information

Analysis and geometry of Markov diffusion operators

Dominique Bakry, Ivan Gentil, Michel Ledoux

（Die Grundlehren der mathematischen Wissenschaften, 348）

Springer, c2014

• : hardback

Note

Includes bibliographical references (p. 527-545) and index

Description and Table of Contents

Description

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 Poincare, 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.

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.Poincare 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.

by "Nielsen BookData"

Details

• NCID: BB14208044
• ISBN:
  • 9783319002262
• LCCN: 2013952461
• Country Code: sz
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: Cham
• Pages/Volumes: xx, 552 p.
• Size: 25 cm
• Classification:
  • DC23 : 519.233
• Subject Headings:
  • LCSH : Markov processes
• Parent Bibliography ID:
  • BA00007422