Dirichlet Forms
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Introduction To The Theory Of Non Symmetric Dirichlet Forms
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Author : Zhi-Ming Ma
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Introduction To The Theory Of Non Symmetric Dirichlet Forms written by Zhi-Ming Ma and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Dirichlet Forms And Analysis On Wiener Space
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Author : Nicolas Bouleau
language : de
Publisher: Walter de Gruyter
Release Date : 2010-10-13
Dirichlet Forms And Analysis On Wiener Space written by Nicolas Bouleau and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-10-13 with Mathematics categories.
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)
Semi Dirichlet Forms And Markov Processes
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Author : Yoichi Oshima
language : en
Publisher: Walter de Gruyter
Release Date : 2013-04-30
Semi Dirichlet Forms And Markov Processes written by Yoichi Oshima and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-30 with Mathematics categories.
This book deals with analytic treatments of Markov processes. Symmetric Dirichlet forms and their associated Markov processes are important and powerful tools in the theory of Markov processes and their applications. The theory is well studied and used in various fields. In this monograph, we intend to generalize the theory to non-symmetric and time dependent semi-Dirichlet forms. By this generalization, we can cover the wide class of Markov processes and analytic theory which do not possess the dual Markov processes. In particular, under the semi-Dirichlet form setting, the stochastic calculus is not well established yet. In this monograph, we intend to give an introduction to such calculus. Furthermore, basic examples different from the symmetric cases are given. The text is written for graduate students, but also researchers.
Dirichlet Forms And Symmetric Markov Processes
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Author : Masatoshi Fukushima
language : en
Publisher: Walter de Gruyter
Release Date : 2011
Dirichlet Forms And Symmetric Markov Processes written by Masatoshi Fukushima and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
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
Hecke S Theory Of Modular Forms And Dirichlet Series
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Author : Bruce C. Berndt
language : en
Publisher: World Scientific
Release Date : 2007
Hecke S Theory Of Modular Forms And Dirichlet Series written by Bruce C. Berndt and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
1. Introduction -- 2. The main correspondence theorem -- 3. A fundamental region -- 4. The case [symbol]> 2 -- 5. The case [symbol]
Introduction To Siegel Modular Forms And Dirichlet Series
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Author : Anatoli Andrianov
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-12-22
Introduction To Siegel Modular Forms And Dirichlet Series written by Anatoli Andrianov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-22 with Mathematics categories.
Several years ago I was invited to an American university to give one-term graduate course on Siegel modular forms, Hecke operators, and related zeta functions. The idea to present in a concise but basically complete and self-contained form an int- duction to an important and developing area based partly on my own work attracted me. I accepted the invitation and started to prepare the course. Unfortunately, the visit was not realized. But the idea of such a course continued to be alive till after a number of years this book was ?nally completed. I hope that this short book will serve to attract young researchers to this beautiful ?eld, and that it will simplify and make more pleasant the initial steps. No special knowledge is presupposed for reading this book beyond standard courses in algebra and calculus (one and several variables), although some skill in working with mathematical texts would be helpful. The reader will judge whether the result was worth the effort. Dedications. The ideas of Goro Shimura exerted a deep in?uence on the number theory of the second half of the twentieth century in general and on the author’s formation in particular. When Andre ` Weil was signing a copy of his “Basic Number Theory” to my son, he wrote in Russian, ”To Fedor Anatolievich hoping that he will become a number theoretist”. Fedor has chosen computer science. Now I pass on the idea to Fedor’s daughter, Alexandra Fedorovna.
New Directions In Dirichlet Forms
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Author : Jürgen Jost
language : en
Publisher: American Mathematical Soc.
Release Date : 1998
New Directions In Dirichlet Forms written by Jürgen Jost and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Dirichlet forms categories.
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.
Graphs And Discrete Dirichlet Spaces
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Author : Matthias Keller
language : en
Publisher: Springer
Release Date : 2021-11-07
Graphs And Discrete Dirichlet Spaces written by Matthias Keller and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-07 with Mathematics categories.
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.
The Theory Of Generalized Dirichlet Forms And Its Applications In Analysis And Stochastics
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Author : Wilhelm Stannat
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
The Theory Of Generalized Dirichlet Forms And Its Applications In Analysis And Stochastics written by Wilhelm Stannat and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
This text explores the theory of generalized Dirichlet Forms along with its applications for analysis and stochastics. Examples are provided.