Analysis And Geometry Of Markov Diffusion Operators PDF Download
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| Author | : Dominique Bakry |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 555 |
| Release | : 2013-11-18 |
| Genre | : Mathematics |
| ISBN | : 3319002279 |
Download Analysis and Geometry of Markov Diffusion Operators Book in PDF, ePub and Kindle
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.
| Author | : Kazuaki Taira |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 196 |
| Release | : 2009-06-30 |
| Genre | : Mathematics |
| ISBN | : 3642016766 |
Download Boundary Value Problems and Markov Processes Book in PDF, ePub and Kindle
This is a thorough and accessible exposition on the functional analytic approach to the problem of construction of Markov processes with Ventcel’ boundary conditions in probability theory. It presents new developments in the theory of singular integrals.
| Author | : Bo'az Klartag |
| Publisher | : Springer Nature |
| Total Pages | : 346 |
| Release | : 2020-06-20 |
| Genre | : Mathematics |
| ISBN | : 3030360202 |
Download Geometric Aspects of Functional Analysis Book in PDF, ePub and Kindle
Continuing the theme of the previous volumes, these seminar notes reflect general trends in the study of Geometric Aspects of Functional Analysis, understood in a broad sense. Two classical topics represented are the Concentration of Measure Phenomenon in the Local Theory of Banach Spaces, which has recently had triumphs in Random Matrix Theory, and the Central Limit Theorem, one of the earliest examples of regularity and order in high dimensions. Central to the text is the study of the Poincaré and log-Sobolev functional inequalities, their reverses, and other inequalities, in which a crucial role is often played by convexity assumptions such as Log-Concavity. The concept and properties of Entropy form an important subject, with Bourgain's slicing problem and its variants drawing much attention. Constructions related to Convexity Theory are proposed and revisited, as well as inequalities that go beyond the Brunn–Minkowski theory. One of the major current research directions addressed is the identification of lower-dimensional structures with remarkable properties in rather arbitrary high-dimensional objects. In addition to functional analytic results, connections to Computer Science and to Differential Geometry are also discussed.
| Author | : K. David Elworthy |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 179 |
| Release | : 2010-11-27 |
| Genre | : Mathematics |
| ISBN | : 303460176X |
Download The Geometry of Filtering Book in PDF, ePub and Kindle
Filtering is the science of nding the law of a process given a partial observation of it. The main objects we study here are di usion processes. These are naturally associated with second-order linear di erential operators which are semi-elliptic and so introduce a possibly degenerate Riemannian structure on the state space. In fact, much of what we discuss is simply about two such operators intertwined by a smooth map, the \projection from the state space to the observations space", and does not involve any stochastic analysis. From the point of view of stochastic processes, our purpose is to present and to study the underlying geometric structure which allows us to perform the ltering in a Markovian framework with the resulting conditional law being that of a Markov process which is time inhomogeneous in general. This geometry is determined by the symbol of the operator on the state space which projects to a symbol on the observation space. The projectible symbol induces a (possibly non-linear and partially de ned) connection which lifts the observation process to the state space and gives a decomposition of the operator on the state space and of the noise. As is standard we can recover the classical ltering theory in which the observations are not usually Markovian by application of the Girsanov- Maruyama-Cameron-Martin Theorem. This structure we have is examined in relation to a number of geometrical topics.
| Author | : Vassili N. Kolokoltsov |
| Publisher | : Walter de Gruyter |
| Total Pages | : 449 |
| Release | : 2011 |
| Genre | : Mathematics |
| ISBN | : 3110250101 |
Download Markov Processes, Semigroups, and Generators Book in PDF, ePub and Kindle
This work offers a highly useful, well developed reference on Markov processes, the universal model for random processes and evolutions. The wide range of applications, in exact sciences as well as in other areas like social studies, require a volume that offers a refresher on fundamentals before conveying the Markov processes and examples for
| Author | : Stefan Hildebrandt |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 663 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3642556272 |
Download Geometric Analysis and Nonlinear Partial Differential Equations Book in PDF, ePub and Kindle
This book is not a textbook, but rather a coherent collection of papers from the field of partial differential equations. Nevertheless we believe that it may very well serve as a good introduction into some topics of this classical field of analysis which, despite of its long history, is highly modem and well prospering. Richard Courant wrote in 1950: "It has always been a temptationfor mathematicians to present the crystallized product of their thought as a deductive general theory and to relegate the individual mathematical phenomenon into the role of an example. The reader who submits to the dogmatic form will be easily indoctrinated. Enlightenment, however, must come from an understanding of motives; live mathematical development springs from specific natural problems which can be easily understood, but whose solutions are difficult and demand new methods or more general significance. " We think that many, if not all, papers of this book are written in this spirit and will give the reader access to an important branch of analysis by exhibiting interest ing problems worth to be studied. Most of the collected articles have an extensive introductory part describing the history of the presented problems as well as the state of the art and offer a well chosen guide to the literature. This way the papers became lengthier than customary these days, but the level of presentation is such that an advanced graduate student should find the various articles both readable and stimulating.
| Author | : Radu Zaharopol |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 1008 |
| Release | : 2005-01-28 |
| Genre | : Mathematics |
| ISBN | : 9783764371340 |
Download Invariant Probabilities of Markov-Feller Operators and Their Supports Book in PDF, ePub and Kindle
This book covers invariant probabilities for a large class of discrete-time homogeneous Markov processes known as Feller processes. These Feller processes appear in the study of iterated function systems with probabilities, convolution operators, and certain time series. From the reviews: "A very useful reference for researchers wishing to enter the area of stationary Markov processes both from a probabilistic and a dynamical point of view." --MONATSHEFTE FÜR MATHEMATIK
| Author | : Michel Ledoux |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 493 |
| Release | : 2013-03-09 |
| Genre | : Mathematics |
| ISBN | : 3642202128 |
Download Probability in Banach Spaces Book in PDF, ePub and Kindle
Isoperimetric, measure concentration and random process techniques appear at the basis of the modern understanding of Probability in Banach spaces. Based on these tools, the book presents a complete treatment of the main aspects of Probability in Banach spaces (integrability and limit theorems for vector valued random variables, boundedness and continuity of random processes) and of some of their links to Geometry of Banach spaces (via the type and cotype properties). Its purpose is to present some of the main aspects of this theory, from the foundations to the most important achievements. The main features of the investigation are the systematic use of isoperimetry and concentration of measure and abstract random process techniques (entropy and majorizing measures). Examples of these probabilistic tools and ideas to classical Banach space theory are further developed.
| Author | : Jürgen Jost |
| Publisher | : Springer |
| Total Pages | : 702 |
| Release | : 2017-10-13 |
| Genre | : Mathematics |
| ISBN | : 3319618601 |
Download Riemannian Geometry and Geometric Analysis Book in PDF, ePub and Kindle
This established reference work continues to provide its readers with a gateway to some of the most interesting developments in contemporary geometry. It offers insight into a wide range of topics, including fundamental concepts of Riemannian geometry, such as geodesics, connections and curvature; the basic models and tools of geometric analysis, such as harmonic functions, forms, mappings, eigenvalues, the Dirac operator and the heat flow method; as well as the most important variational principles of theoretical physics, such as Yang-Mills, Ginzburg-Landau or the nonlinear sigma model of quantum field theory. The present volume connects all these topics in a systematic geometric framework. At the same time, it equips the reader with the working tools of the field and enables her or him to delve into geometric research. The 7th edition has been systematically reorganized and updated. Almost no page has been left unchanged. It also includes new material, for instance on symplectic geometry, as well as the Bishop-Gromov volume growth theorem which elucidates the geometric role of Ricci curvature. From the reviews:“This book provides a very readable introduction to Riemannian geometry and geometric analysis... With the vast development of the mathematical subject of geometric analysis, the present textbook is most welcome.” Mathematical Reviews “For readers familiar with the basics of differential geometry and some acquaintance with modern analysis, the book is reasonably self-contained. The book succeeds very well in laying out the foundations of modern Riemannian geometry and geometric analysis. It introduces a number of key techniques and provides a representative overview of the field.” Monatshefte für Mathematik
| Author | : Hershel M. Farkas |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 563 |
| Release | : 2012-09-18 |
| Genre | : Mathematics |
| ISBN | : 1461440750 |
Download From Fourier Analysis and Number Theory to Radon Transforms and Geometry Book in PDF, ePub and Kindle
A memorial conference for Leon Ehrenpreis was held at Temple University, November 15-16, 2010. In the spirit of Ehrenpreis’s contribution to mathematics, the papers in this volume, written by prominent mathematicians, represent the wide breadth of subjects that Ehrenpreis traversed in his career, including partial differential equations, combinatorics, number theory, complex analysis and a bit of applied mathematics. With the exception of one survey article, the papers in this volume are all new results in the various fields in which Ehrenpreis worked . There are papers in pure analysis, papers in number theory, papers in what may be called applied mathematics such as population biology and parallel refractors and papers in partial differential equations. The mature mathematician will find new mathematics and the advanced graduate student will find many new ideas to explore.A biographical sketch of Leon Ehrenpreis by his daughter, a professional journalist, enhances the memorial tribute and gives the reader a glimpse into the life and career of a great mathematician.
