Download or read book Functional Inequalities Markov Semigroups and Spectral Theory written by Fengyu Wang and published by Elsevier. This book was released on 2006-04-06 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, the functional inequalities are introduced to describe:(i) the spectrum of the generator: the essential and discrete spectrums, high order eigenvalues, the principle eigenvalue, and the spectral gap;(ii) the semigroup properties: the uniform intergrability, the compactness, the convergence rate, and the existence of density;(iii) the reference measure and the intrinsic metric: the concentration, the isoperimetic inequality, and the transportation cost inequality.

Download or read book Stochastic Spectral Theory for Selfadjoint Feller Operators written by Michael Demuth and published by Birkhäuser. This book was released on 2012-12-06 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, a beautiful interplay between probability theory (Markov processes, martingale theory) on the one hand and operator and spectral theory on the other yields a uniform treatment of several kinds of Hamiltonians such as the Laplace operator, relativistic Hamiltonian, Laplace-Beltrami operator, and generators of Ornstein-Uhlenbeck processes. The unified approach provides a new viewpoint of and a deeper insight into the subject.

Download or read book Analysis and Geometry of Markov Diffusion Operators written by Dominique Bakry and published by Springer Science & Business Media. This book was released on 2013-11-18 with total page 555 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Hilbert C Modules and Quantum Markov Semigroups written by Lunchuan Zhang and published by Springer Nature. This book was released on with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Heat Kernels and Spectral Theory written by E. B. Davies and published by Cambridge University Press. This book was released on 1989 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: Heat Kernels and Spectral Theory investigates the theory of second-order elliptic operators.

Download or read book Analytical Methods for Kolmogorov Equations written by Luca Lorenzi and published by CRC Press. This book was released on 2016-10-04 with total page 572 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second edition of this book has a new title that more accurately reflects the table of contents. Over the past few years, many new results have been proven in the field of partial differential equations. This edition takes those new results into account, in particular the study of nonautonomous operators with unbounded coefficients, which has received great attention. Additionally, this edition is the first to use a unified approach to contain the new results in a singular place.

Download or read book Festschrift Masatoshi Fukushima written by Zhen-Qing Chen and published by World Scientific. This book was released on 2014-11-27 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains original research papers by leading experts in the fields of probability theory, stochastic analysis, potential theory and mathematical physics. There is also a historical account on Masatoshi Fukushima's contribution to mathematics, as well as authoritative surveys on the state of the art in the field. Contents:Professor Fukushima's Work:The Mathematical Work of Masatoshi Fukushima — An Essay (Zhen-Qing Chen, Niels Jacob, Masayoshi Takeda and Toshihiro Uemura)Bibliography of Masatoshi FukushimaContributions:Quasi Regular Dirichlet Forms and the Stochastic Quantization Problem (Sergio Albeverio, Zhi-Ming Ma and Michael Röckner)Comparison of Quenched and Annealed Invariance Principles for Random Conductance Model: Part II (Martin Barlow, Krzysztof Burdzy and Adám Timár)Some Historical Aspects of Error Calculus by Dirichlet Forms (Nicolas Bouleau)Stein's Method, Malliavin Calculus, Dirichlet Forms and the Fourth Moment Theorem (Louis H Y Chen and Guillaume Poly)Progress on Hardy-Type Inequalities (Mu-Fa Chen)Functional Inequalities for Pure-Jump Dirichlet Forms (Xin Chen, Feng-Yu Wang and Jian Wang)Additive Functionals and Push Forward Measures Under Veretennikov's Flow (Shizan Fang and Andrey Pilipenko)On a Result of D W Stroock (Patrick J Fitzsimmons)Consistent Risk Measures and a Non-Linear Extension of Backwards Martingale Convergence (Hans Föllmer and Irina Penner)Unavoidable Collections of Balls for Processes with Isotropic Unimodal Green Function (Wolfhard Hansen)Functions of Locally Bounded Variation on Wiener Spaces (Masanori Hino)A Dirichlet Space on Ends of Tree and Superposition of Nodewise Given Dirichlet Forms with Tier Linkage (Hiroshi Kaneko)Dirichlet Forms in Quantum Theory (Witold Karwowski and Ludwig Streit)On a Stability of Heat Kernel Estimates under Generalized Non-Local Feynman-Kac Perturbations for Stable-Like Processes (Daehong Kim and Kazuhiro Kuwae)Martin Boundary for Some Symmetric Lévy Processes (Panki Kim, Renming Song and Zoran Vondraček)Level Statistics of One-Dimensional Schrödinger Operators with Random Decaying Potential (Shinichi Kotani and Fumihiko Nakano)Perturbation of the Loop Measure (Yves Le Jan and Jay Rosen)Regular Subspaces of Dirichlet Forms (Liping Li and Jiangang Ying)Quasi-Regular Semi-Dirichlet Forms and Beyond (Zhi-Ming Ma, Wei Sun and Li-Fei Wang)Large Deviation Estimates for Controlled Semi-Martingales (Hideo Nagai)A Comparison Theorem for Backward SPDEs with Jumps (Bernt Øksendal, Agnès Sulem and Tusheng Zhang)On a Construction of a Space-Time Diffusion Process with Boundary Condition (Yoichi Oshima)Lower Bounded Semi-Dirichlet Forms Associated with Lévy Type Operators (René L Schilling and Jian Wang)Ultracontractivity for Non-Symmetric Markovian Semigroups (Ichiro Shigekawa)Metric Measure Spaces with Variable Ricci Bounds and Couplings of Brownian Motions (Karl-Theodor Sturm)Intrinsic Ultracontractivity and Semi-Small Perturbation for Skew Product Diffusion Operators (Matsuyo Tomisaki) Readership: Researchers in probability, stochastic analysis and mathematical physics. Key Features:Research papers by leading expertsHistorical account of M Fukushima's contribution to mathematicsAuthoritative surveys on the state of the art in the fieldKeywords:Probability Theory;Markov Processes;Dirichlet Forms;Potential Theory;Mathematical Physics

Download or read book Analysis for Diffusion Processes on Riemannian Manifolds written by Feng-Yu Wang and published by World Scientific. This book was released on 2013-09-23 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic analysis on Riemannian manifolds without boundary has been well established. However, the analysis for reflecting diffusion processes and sub-elliptic diffusion processes is far from complete. This book contains recent advances in this direction along with new ideas and efficient arguments, which are crucial for further developments. Many results contained here (for example, the formula of the curvature using derivatives of the semigroup) are new among existing monographs even in the case without boundary. Contents:PreliminariesDiffusion Processes on Riemannian Manifolds without BoundaryReflecting Diffusion Processes on Manifolds with BoundaryStochastic Analysis on Path Space over Manifolds with BoundarySubelliptic Diffusion Processes Readership: Graduate students, researchers and professionals in probability theory, differential geometry and partial differential equations. Keywords:Diffusion Pocess;Reflecting Diffusion Process;Neumann Semigroup;Curvature;Second Fundamental Form;ManifoldKey Features:First book where the key theory and machinery of the reflecting diffusion processes on Riemannian manifolds with boundary are systematically introducedFirst book to clarify intrinsic links between the semigroup properties on one hand and geometric quantities (curvature and second fundamental form) on the other, and these links are introduced in an easy to understand manner: by formulating geometric quantities using short time behaviors of derivatives of the semigroup, whereby a reader can easily comprehend the equivalence of semigroup properties associated with lower bounds of these geometric quantitiesFirst book where stochastic analysis on Riemannian manifolds with boundary are introduced

Download or read book Fokker Planck Kolmogorov Equations written by Vladimir I. Bogachev and published by American Mathematical Soc.. This book was released on 2015-12-17 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an exposition of the principal concepts and results related to second order elliptic and parabolic equations for measures, the main examples of which are Fokker-Planck-Kolmogorov equations for stationary and transition probabilities of diffusion processes. Existence and uniqueness of solutions are studied along with existence and Sobolev regularity of their densities and upper and lower bounds for the latter. The target readership includes mathematicians and physicists whose research is related to diffusion processes as well as elliptic and parabolic equations.

Download or read book The Poisson Dirichlet Distribution and Related Topics written by Shui Feng and published by Springer Science & Business Media. This book was released on 2010-05-27 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting a comprehensive study of the Poisson-Dirichlet distribution, this volume emphasizes recent progress in evolutionary dynamics and asymptotic behaviors. The self-contained text presents methods and techniques that appeal to researchers in a wide variety of subjects.

Download or read book Spectral Theory Function Spaces and Inequalities written by B. Malcolm Brown and published by Springer Science & Business Media. This book was released on 2011-11-06 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a collection of contributed papers which focus on recent results in areas of differential equations, function spaces, operator theory and interpolation theory. In particular, it covers current work on measures of non-compactness and real interpolation, sharp Hardy-Littlewood-Sobolev inequalites, the HELP inequality, error estimates and spectral theory of elliptic operators, pseudo differential operators with discontinuous symbols, variable exponent spaces and entropy numbers. These papers contribute to areas of analysis which have been and continue to be heavily influenced by the leading British analysts David Edmunds and Des Evans. This book marks their respective 80th and 70th birthdays.

Download or read book Harnack Inequalities for Stochastic Partial Differential Equations written by Feng-Yu Wang and published by Springer Science & Business Media. This book was released on 2013-08-13 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: ​In this book the author presents a self-contained account of Harnack inequalities and applications for the semigroup of solutions to stochastic partial and delayed differential equations. Since the semigroup refers to Fokker-Planck equations on infinite-dimensional spaces, the Harnack inequalities the author investigates are dimension-free. This is an essentially different point from the above mentioned classical Harnack inequalities. Moreover, the main tool in the study is a new coupling method (called coupling by change of measures) rather than the usual maximum principle in the current literature.

Download or read book Optimal Transportation written by Yann Ollivier and published by Cambridge University Press. This book was released on 2014-08-07 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lecture notes and research papers on optimal transportation, its applications, and interactions with other areas of mathematics.

Download or read book Surveys in Stochastic Processes written by Jochen Blath and published by European Mathematical Society. This book was released on 2011 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 33rd Bernoulli Society Conference on Stochastic Processes and Their Applications was held in Berlin from July 27 to July 31, 2009. It brought together more than 600 researchers from 49 countries to discuss recent progress in the mathematical research related to stochastic processes, with applications ranging from biology to statistical mechanics, finance and climatology. This book collects survey articles highlighting new trends and focal points in the area written by plenary speakers of the conference, all of them outstanding international experts. A particular aim of this collection is to inspire young scientists to pursue research goals in the wide range of fields represented in this volume.

Download or read book Spectral Theory Function Spaces and Inequalities written by B. Malcolm Brown and published by Birkhäuser. This book was released on 2011-11-09 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a collection of contributed papers which focus on recent results in areas of differential equations, function spaces, operator theory and interpolation theory. In particular, it covers current work on measures of non-compactness and real interpolation, sharp Hardy-Littlewood-Sobolev inequalites, the HELP inequality, error estimates and spectral theory of elliptic operators, pseudo differential operators with discontinuous symbols, variable exponent spaces and entropy numbers. These papers contribute to areas of analysis which have been and continue to be heavily influenced by the leading British analysts David Edmunds and Des Evans. This book marks their respective 80th and 70th birthdays.

Download or read book Semigroups of Operators and Spectral Theory written by S Kantorovitz and published by CRC Press. This book was released on 1995-06-19 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents some aspects of the theory of semigroups of operators, mostly from the point of view of its interaction withspectral theory. In order to make it self-contained, a concise description of the basic theory of semigroups, with complete proofs, is included in Part I. Some of the author's recent results, such as the construction of the Hille-Yosida space for general operators, the semi-simplicity manifold, and a Taylor formula for semigroups as functions of their generator, are also included in Part I. Part II describes recent generalizations (most of them in bookform for the first time), including pre-semigroups, semi-simplicity manifolds in situations more general than that considered in Part I, semigroups of unbounded symmetric operators, and an analogous result on "local cosine families" and semi-analytic vectors. It is hoped that this book will inspire more research in this field. This book will be of particular interest to graduate students and researchers working operator theory and its applications.

Download or read book Optimal Transport written by Yann Ollivier and published by Cambridge University Press. This book was released on 2014-08-07 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of optimal transportation has its origins in the eighteenth century when the problem of transporting resources at a minimal cost was first formalised. Through subsequent developments, particularly in recent decades, it has become a powerful modern theory. This book contains the proceedings of the summer school 'Optimal Transportation: Theory and Applications' held at the Fourier Institute in Grenoble. The event brought together mathematicians from pure and applied mathematics, astrophysics, economics and computer science. Part I of this book is devoted to introductory lecture notes accessible to graduate students, while Part II contains research papers. Together, they represent a valuable resource on both fundamental and advanced aspects of optimal transportation, its applications, and its interactions with analysis, geometry, PDE and probability, urban planning and economics. Topics covered include Ricci flow, the Euler equations, functional inequalities, curvature-dimension conditions, and traffic congestion.