TY - BOOK ID - 14220914 TI - Analysis and Geometry of Markov Diffusion Operators AU - Bakry, Dominique. AU - Gentil, Ivan. AU - Ledoux, Michel. PY - 2014 SN - 3319002260 3319002279 PB - Cham : Springer International Publishing : Imprint: Springer, DB - UniCat KW - Markov operators. KW - Markov processes. KW - Analysis, Markov KW - Chains, Markov KW - Markoff processes KW - Markov analysis KW - Markov chains KW - Markov models KW - Models, Markov KW - Processes, Markov KW - Operators, Markov KW - Mathematics. KW - Mathematical analysis. KW - Analysis (Mathematics). KW - Functional analysis. KW - Partial differential equations. KW - Differential geometry. KW - Probabilities. KW - Analysis. KW - Probability Theory and Stochastic Processes. KW - Differential Geometry. KW - Partial Differential Equations. KW - Functional Analysis. KW - Ergodic theory KW - Linear operators KW - Markov processes KW - Stochastic processes KW - Global analysis (Mathematics). KW - Distribution (Probability theory. KW - Global differential geometry. KW - Differential equations, partial. KW - Functional calculus KW - Calculus of variations KW - Functional equations KW - Integral equations KW - Partial differential equations KW - Geometry, Differential KW - Distribution functions KW - Frequency distribution KW - Characteristic functions KW - Probabilities KW - Analysis, Global (Mathematics) KW - Differential topology KW - Functions of complex variables KW - Geometry, Algebraic KW - Differential geometry KW - Probability KW - Statistical inference KW - Combinations KW - Mathematics KW - Chance KW - Least squares KW - Mathematical statistics KW - Risk KW - 517.1 Mathematical analysis KW - Mathematical analysis UR - https://www.unicat.be/uniCat?func=search&query=sysid:14220914 AB - 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. ER -