Bakry, J. Grundlehren der Mathematischen Wissenschaften , vol. Ledoux, Analysis and geometry of Markov diffusion operators. Springer, Berlin Bakry, D. MR g D. Baudoin, J. Wang, Curvature dimension inequalities and Grundlehren der Mathematischen Wissenschaften , vol Springer, Cham, 8.
Ball, An elementary introduction to modern convex geometry. Analysis and geometry of Markov diffusion operators , volume of Grundlehren der Mathematischen Wissenschaften. Bakry, D. Springer, Cham 7. Grundlehren der mathematischen Wissenschaften , vol. Springer, Berlin Benamou, J. Analysis and geometry of Markov diffusion operators. Springer, Cham, Barthe, D.
Cordero—Erausquin and B. Trapani, Partial inner product spaces, metric operators and generalized Hermiticity, Analysis and geometry of Markov diffusion operators , Grundlehren der Mathematischen Wissenschaften [Fundamental In Methods of functional analysis and theory of elliptic equations Naples, , pages 19— Analysis and geometry of Markov diffusion operators , volume of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles 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 : Dan Crisan Publisher: Springer ISBN: Category: Mathematics Page: View: Read Now » Articles from many of the main contributors to recent progress in stochastic analysis are included in this volume, which provides a snapshot of the current state of the area and its ongoing developments.
It constitutes the proceedings of the conference on "Stochastic Analysis and Applications" held at the University of Oxford and the Oxford-Man Institute during September, Terry Lyons is one of the leaders in the field of stochastic analysis. His introduction of the notion of rough paths has revolutionized the field, both in theory and in practice. Stochastic Analysis is the branch of mathematics that deals with the analysis of dynamical systems affected by noise.
It emerged as a core area of mathematics in the late 20th century and has subsequently developed into an important theory with a wide range of powerful and novel tools, and with impressive applications within and beyond mathematics. Many systems are profoundly affected by stochastic fluctuations and it is not surprising that the array of applications of Stochastic Analysis is vast and touches on many aspects of life.
The present volume is intended for researchers and Ph. Thomas, Minneapolis, Minnesota. Over the last decade there has been a resurgence of interest in problems involving nonlocal operators, motivated by applications in many areas such as analysis, geometry, and stochastic processes. Problems represented in this volume include uniqueness for weak solutions to abstract parabolic equations with fractional time derivatives, the behavior of the one-phase Bernoulli-type free boundary near a fixed boundary and its relation to a Signorini-type problem, connections between fractional powers of the spherical Laplacian and zeta functions from the analytic number theory and differential geometry, and obstacle problems for a class of not stable-like nonlocal operators for asset price models widely used in mathematical finance.
The volume also features a comprehensive introduction to various aspects of the fractional Laplacian, with many historical remarks and an extensive list of references, suitable for beginners and more seasoned researchers alike. Starting from basic notions, the authors of these lecture notes accompany the reader on a journey up to the latest research, highlighting new challenges and addressing unsolved problems at the interface between mathematics and physics.
Though the book is primarily addressed to graduate students, it will also be of interest to researchers. Written by experts in the field, this book is a valuable tool for the advanced mathematician. This well-known and intensively studied model carries a rich and beautiful mathematical structure, which is uncovered here in a systematic manner.
In addition to approaches by means of analysis, combinatorics and PDE, a geometric perspective is brought in through Amari's and Chentsov's information geometry. This concept allows us to calculate many quantities of interest systematically; likewise, the employed global perspective elucidates the stratification of the model in an unprecedented manner. Furthermore, the links to statistical mechanics and large deviation theory are explored and developed into powerful tools.
The GL series does not strive for systematic coverage of all of mathematics. There are both overlaps between books and gaps. However, a systematic effort is made to cover important areas of current interest in a GL volume when they become ripe for GL-type treatment.
Editorial board. The tastes of the editors play a pivotal role in the selection of topics. As far as the development of mathematics permits, the direction of GL remains true to the original spirit of Courant.
Many of the oldest volumes are popular to this day and some have not been superseded. One should perhaps never advertise a contemporary book as a classic but many recent volumes and many forthcoming volumes will surely earn this attribute through their use by generations of mathematicians.
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