Download or read book Dirichlet Forms and Related Topics written by Zhen-Qing Chen and published by Springer Nature. This book was released on 2022-09-04 with total page 572 pages. Available in PDF, EPUB and Kindle. Book excerpt: This conference proceeding contains 27 peer-reviewed invited papers from leading experts as well as young researchers all over the world in the related fields that Professor Fukushima has made important contributions to. These 27 papers cover a wide range of topics in probability theory, ranging from Dirichlet form theory, Markov processes, heat kernel estimates, entropy on Wiener spaces, analysis on fractal spaces, random spanning tree and Poissonian loop ensemble, random Riemannian geometry, SLE, space-time partial differential equations of higher order, infinite particle systems, Dyson model, functional inequalities, branching process, to machine learning and Hermitizable problems for complex matrices. Researchers and graduate students interested in these areas will find this book appealing.
Download or read book Dirichlet Forms and Related Topics written by Zhen-Qing Chen and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This conference proceeding contains 27 peer-reviewed invited papers from leading experts as well as young researchers all over the world in the related fields that Professor Fukushima has made important contributions to. These 27 papers cover a wide range of topics in probability theory, ranging from Dirichlet form theory, Markov processes, heat kernel estimates, entropy on Wiener spaces, analysis on fractal spaces, random spanning tree and Poissonian loop ensemble, random Riemannian geometry, SLE, space-time partial differential equations of higher order, infinite particle systems, Dyson model, functional inequalities, branching process, to machine learning and Hermitizable problems for complex matrices. Researchers and graduate students interested in these areas will find this book appealing. Professor Masatoshi Fukushima is well known for his fundamental contributions to the theory of Dirichlet forms and symmetric Markov processes.
Download or read book New Directions in Dirichlet Forms written by Jürgen Jost and published by American Mathematical Soc.. This book was released on 1998 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of Dirichlet forms brings together methods and insights from the calculus of variations, sotchastic analysis, partial differential and difference equations, potential theory, Riemannian geometry and more. This book features contributions by leading experts and provides up-to-date, authoritative accounts on exciting developments in the field and on new research perspectives. Topics covered include the following: stochastic analysis on configuration spaces, specifically a mathematically rigorous approach to the stochastic dynamics of Gibbs measures and infinite interacting particle systems; subelliptic PDE, homogenization, and fractals; geometric aspects of Dirichlet forms on metric spaces and function theory on such spaces; generalized harmonic maps as nonlinear analogues of Dirichlet forms, with an emphasis on non-locally compact situations; and a stochastic approach based on Brownian motion to harmonic maps and their regularity. Various new connections between the topics are featured, and it is demonstarted that the theory of Dirichlet forms provides the proper framework for exploring these connections. Titles in this series are co-published with International Press, Cambridge, MA.
Download or read book Dirichlet Forms and Analysis on Wiener Space written by Nicolas Bouleau and published by Walter de Gruyter. This book was released on 2010-10-13 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of this book is analysis on Wiener space by means of Dirichlet forms and Malliavin calculus. There are already several literature on this topic, but this book has some different viewpoints. First the authors review the theory of Dirichlet forms, but they observe only functional analytic, potential theoretical and algebraic properties. They do not mention the relation with Markov processes or stochastic calculus as discussed in usual books (e.g. Fukushima’s book). Even on analytic properties, instead of mentioning the Beuring-Deny formula, they discuss “carré du champ” operators introduced by Meyer and Bakry very carefully. Although they discuss when this “carré du champ” operator exists in general situation, the conditions they gave are rather hard to verify, and so they verify them in the case of Ornstein-Uhlenbeck operator in Wiener space later. (It should be noticed that one can easily show the existence of “carré du champ” operator in this case by using Shigekawa’s H-derivative.) In the part on Malliavin calculus, the authors mainly discuss the absolute continuity of the probability law of Wiener functionals. The Dirichlet form corresponds to the first derivative only, and so it is not easy to consider higher order derivatives in this framework. This is the reason why they discuss only the first step of Malliavin calculus. On the other hand, they succeeded to deal with some delicate problems (the absolute continuity of the probability law of the solution to stochastic differential equations with Lipschitz continuous coefficients, the domain of stochastic integrals (Itô-Ramer-Skorokhod integrals), etc.). This book focuses on the abstract structure of Dirichlet forms and Malliavin calculus rather than their applications. However, the authors give a lot of exercises and references and they may help the reader to study other topics which are not discussed in this book. Zentralblatt Math, Reviewer: S.Kusuoka (Hongo)
Download or read book Dirichlet Forms and Symmetric Markov Processes written by Masatoshi Fukushima and published by Walter de Gruyter. This book was released on 2011 with total page 501 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the publication of the first edition in 1994, this book has attracted constant interests from readers and is by now regarded as a standard reference for the theory of Dirichlet forms. For the present second edition, the authors not only revise
Download or read book Dirichlet Forms and Stochastic Processes written by Zhiming Ma and published by Walter de Gruyter. This book was released on 2011-06-24 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
Download or read book New Trends in Stochastic Analysis and Related Topics written by Huaizhong Zhao and published by World Scientific. This book was released on 2012 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: The volume is dedicated to Professor David Elworthy to celebrate his fundamental contribution and exceptional influence on stochastic analysis and related fields. Stochastic analysis has been profoundly developed as a vital fundamental research area in mathematics in recent decades. It has been discovered to have intrinsic connections with many other areas of mathematics such as partial differential equations, functional analysis, topology, differential geometry, dynamical systems, etc. Mathematicians developed many mathematical tools in stochastic analysis to understand and model random phenomena in physics, biology, finance, fluid, environment science, etc. This volume contains 12 comprehensive review/new articles written by world leading researchers (by invitation) and their collaborators. It covers stochastic analysis on manifolds, rough paths, Dirichlet forms, stochastic partial differential equations, stochastic dynamical systems, infinite dimensional analysis, stochastic flows, quantum stochastic analysis and stochastic Hamilton Jacobi theory. Articles contain cutting edge research methodology, results and ideas in relevant fields. They are of interest to research mathematicians and postgraduate students in stochastic analysis, probability, partial differential equations, dynamical systems, mathematical physics, as well as to physicists, financial mathematicians, engineers, etc.
Download or read book Graphs and Discrete Dirichlet Spaces written by Matthias Keller and published by Springer Nature. This book was released on 2021-10-22 with total page 675 pages. Available in PDF, EPUB and Kindle. Book excerpt: The spectral geometry of infinite graphs deals with three major themes and their interplay: the spectral theory of the Laplacian, the geometry of the underlying graph, and the heat flow with its probabilistic aspects. In this book, all three themes are brought together coherently under the perspective of Dirichlet forms, providing a powerful and unified approach. The book gives a complete account of key topics of infinite graphs, such as essential self-adjointness, Markov uniqueness, spectral estimates, recurrence, and stochastic completeness. A major feature of the book is the use of intrinsic metrics to capture the geometry of graphs. As for manifolds, Dirichlet forms in the graph setting offer a structural understanding of the interaction between spectral theory, geometry and probability. For graphs, however, the presentation is much more accessible and inviting thanks to the discreteness of the underlying space, laying bare the main concepts while preserving the deep insights of the manifold case. Graphs and Discrete Dirichlet Spaces offers a comprehensive treatment of the spectral geometry of graphs, from the very basics to deep and thorough explorations of advanced topics. With modest prerequisites, the book can serve as a basis for a number of topics courses, starting at the undergraduate level.
Download or read book Dirichlet Forms and Symmetric Markov Processes written by Masatoshi Fukushima and published by . This book was released on 1994 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 35 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob. Titles in planning include Flavia Smarazzo and Alberto Tesei, Measure Theory: Radon Measures, Young Measures, and Applications to Parabolic Problems (2019) Elena Cordero and Luigi Rodino, Time-Frequency Analysis of Operators (2019) Mark M. Meerschaert, Alla Sikorskii, and Mohsen Zayernouri, Stochastic and Computational Models for Fractional Calculus, second edition (2020) Mariusz Lemańczyk, Ergodic Theory: Spectral Theory, Joinings, and Their Applications (2020) Marco Abate, Holomorphic Dynamics on Hyperbolic Complex Manifolds (2021) Miroslava Antić, Joeri Van der Veken, and Luc Vrancken, Differential Geometry of Submanifolds: Submanifolds of Almost Complex Spaces and Almost Product Spaces (2021) Kai Liu, Ilpo Laine, and Lianzhong Yang, Complex Differential-Difference Equations (2021) Rajendra Vasant Gurjar, Kayo Masuda, and Masayoshi Miyanishi, Affine Space Fibrations (2022)
Download or read book Stochastic Analysis and Related Topics written by H. Körezlioglu and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a large spectrum of work: super processes, Dirichlet forms, anticipative stochastic calculus, random fields and Wiener space analysis. The first part of the volume consists of two main lectures given at the third Silivri meeting in 1990: 1. "Infinitely divisible random measures and superprocesses" by D.A. Dawson, 2. "Dirichlet forms on infinite dimensional spaces and appli cations" by M. Rockner. The second part consists of recent research papers all related to Stochastic Analysis, motivated by stochastic partial differ ential equations, Markov fields, the Malliavin calculus and the Feynman path integrals. We would herewith like to thank the ENST for its material support for the above mentioned meeting as well as for the ini tial preparation of this volume and to our friend and colleague Erhan Qmlar whose help and encouragement for the realization of this volume have been essential. H. Korezlioglu A.S. Ustiinel INFINITELY DIVISIBLE RANDOM MEASURES AND SUPERPROCESSES DONALD A. DAWSON 1. Introduction.
Download or read book Introduction to the Theory of Non Symmetric Dirichlet Forms written by Zhi-Ming Ma and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to give a streamlined introduction to the theory of (not necessarily symmetric) Dirichlet forms on general state spaces. It includes both the analytic and the probabilistic part of the theory up to and including the construction of an associated Markov process. It is based on recent joint work of S. Albeverio and the two authors and on a one-year-course on Dirichlet forms taught by the second named author at the University of Bonn in 1990/9l. It addresses both researchers and graduate students who require a quick but complete introduction to the theory. Prerequisites are a basic course in probabil ity theory (including elementary martingale theory up to the optional sampling theorem) and a sound knowledge of measure theory (as, for example, to be found in Part I of H. Bauer [B 78]). Furthermore, an elementary course on lin ear operators on Banach and Hilbert spaces (but without spectral theory) and a course on Markov processes would be helpful though most of the material needed is included here.
Download or read book New Directions in Dirichlet Forms written by and published by . This book was released on 1998 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Dirichlet Forms written by E. Fabes and published by Springer. This book was released on 2006-11-15 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of Dirichlet forms has witnessed recently some very important developments both in theoretical foundations and in applications (stochasticprocesses, quantum field theory, composite materials,...). It was therefore felt timely to have on this subject a CIME school, in which leading experts in the field would present both the basic foundations of the theory and some of the recent applications. The six courses covered the basic theory and applications to: - Stochastic processes and potential theory (M. Fukushima and M. Roeckner) - Regularity problems for solutions to elliptic equations in general domains (E. Fabes and C. Kenig) - Hypercontractivity of semigroups, logarithmic Sobolev inequalities and relation to statistical mechanics (L. Gross and D. Stroock). The School had a constant and active participation of young researchers, both from Italy and abroad.
Download or read book Topics on Concentration Phenomena and Problems with Multiple Scales written by Andrea Braides and published by Springer Science & Business Media. This book was released on 2006-11-22 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of variational problems showing multi-scale behaviour with oscillation or concentration phenomena is a challenging topic of very active research. This volume collects lecture notes on the asymptotic analysis of such problems when multi-scale behaviour derives from scale separation in the passage from atomistic systems to continuous functionals, from competition between bulk and surface energies, from various types of homogenization processes, and on concentration effects in Ginzburg-Landau energies and in subcritical growth problems.
Download or read book Elementary Dirichlet Series and Modular Forms written by Goro Shimura and published by Springer Science & Business Media. This book was released on 2007-08-06 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt: A book on any mathematical subject beyond the textbook level is of little value unless it contains new ideas and new perspectives. It helps to include new results, provided that they give the reader new insights and are presented along with known old results in a clear exposition. It is with this philosophy that the author writes this volume. The two subjects, Dirichlet series and modular forms, are traditional subjects, but here they are treated in both orthodox and unorthodox ways. Regardless of the unorthodox treatment, the author has made the book accessible to those who are not familiar with such topics by including plenty of expository material.
Download or read book Multiple Dirichlet Series L functions and Automorphic Forms written by Daniel Bump and published by Springer. This book was released on 2012-07-09 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multiple Dirichlet Series, L-functions and Automorphic Forms gives the latest advances in the rapidly developing subject of Multiple Dirichlet Series, an area with origins in the theory of automorphic forms that exhibits surprising and deep connections to crystal graphs and mathematical physics. As such, it represents a new way in which areas including number theory, combinatorics, statistical mechanics, and quantum groups are seen to fit together. The volume also includes papers on automorphic forms and L-functions and related number-theoretic topics. This volume will be a valuable resource for graduate students and researchers in number theory, combinatorics, representation theory, mathematical physics, and special functions. Contributors: J. Beineke, B. Brubaker, D. Bump, G. Chinta, G. Cornelissen, C.A. Diaconu, S. Frechette, S. Friedberg, P. Garrett, D. Goldfeld, P.E. Gunnells, B. Heim, J. Hundley, D. Ivanov, Y. Komori, A.V. Kontorovich, O. Lorscheid, K. Matsumoto, P.J. McNamara, S.J. Patterson, M. Suzuki, H. Tsumura.
Download or read book Theory of Generalized Dirichlet Forms and Its Applications in Analysis and Stochasticse written by Wilhelm Stannat and published by . This book was released on 2014-09-11 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text explores the theory of generalized Dirichlet Forms along with its applications for analysis and stochastics. Examples are provided.
