New Directions In Dirichlet Forms
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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.
New Directions In Dirichlet Forms
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Author :
language : en
Publisher:
Release Date : 1998
New Directions In Dirichlet Forms written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Dirichlet forms categories.
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)
Dirichlet Forms
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Author : E. Fabes
language : en
Publisher: Springer
Release Date : 2006-11-15
Dirichlet Forms written by E. Fabes and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
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.
Hyperfinite Dirichlet Forms And Stochastic Processes
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Author : Sergio Albeverio
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-05-27
Hyperfinite Dirichlet Forms And Stochastic Processes written by Sergio Albeverio 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 2011-05-27 with Mathematics categories.
This monograph treats the theory of Dirichlet forms from a comprehensive point of view, using "nonstandard analysis." Thus, it is close in spirit to the discrete classical formulation of Dirichlet space theory by Beurling and Deny (1958). The discrete infinitesimal setup makes it possible to study the diffusion and the jump part using essentially the same methods. This setting has the advantage of being independent of special topological properties of the state space and in this sense is a natural one, valid for both finite- and infinite-dimensional spaces. The present monograph provides a thorough treatment of the symmetric as well as the non-symmetric case, surveys the theory of hyperfinite Lévy processes, and summarizes in an epilogue the model-theoretic genericity of hyperfinite stochastic processes theory.
The Theory Of Generalized Dirichlet Forms And Its Applications In Analysis And Stochastics
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Author : Wilhelm Stannat
language : de
Publisher:
Release Date : 1997
The Theory Of Generalized Dirichlet Forms And Its Applications In Analysis And Stochastics written by Wilhelm Stannat and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with categories.
New Directions In Function Theory From Complex To Hypercomplex To Non Commutative
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Author : Daniel Alpay
language : en
Publisher: Springer Nature
Release Date : 2022-01-01
New Directions In Function Theory From Complex To Hypercomplex To Non Commutative written by Daniel Alpay and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-01 with Mathematics categories.
This volume presents selected contributions from experts gathered at Chapman University for a conference held in November 2019 on new directions in function theory. The papers, written by leading researchers in the field, relate to hypercomplex analysis, Schur analysis and de Branges spaces, new aspects of classical function theory, and infinite dimensional analysis. Signal processing constitutes a strong presence in several of the papers.A second volume in this series of conferences, this book will appeal to mathematicians interested in learning about new fields of development in function theory.
Stochastic Processes Physics And Geometry New Interplays I
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Author : Sergio Albeverio
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Stochastic Processes Physics And Geometry New Interplays I written by Sergio Albeverio 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 2000 with Mathematics categories.
This volume and "IStochastic Processes, Physics and Geometry: New Interplays II" present state-of-the-art research currently unfolding at the interface between mathematics and physics. Included are select articles from the international conference held in Leipzig (Germany) in honor of Sergio Albeverio's sixtieth birthday. The theme of the conference, "Infinite Dimensional (Stochastic) Analysis and Quantum Physics", was chosen to reflect Albeverio's wide-ranging scientific interests. The articles in these books reflect that broad range of interests and provide a detailed overview highlighting the deep interplay among stochastic processes, mathematical physics, and geometry. The contributions are written by internationally recognized experts in the fields of stochastic analysis, linear and nonlinear (deterministic and stochastic) PDEs, infinite dimensional analysis, functional analysis, commutative and noncommutative probability theory, integrable systems, quantum and statistical mechanics, geometric quantization, and neural networks. Also included are applications in biology and other areas. Most of the contributions are high-level research papers. However, there are also some overviews on topics of general interest. The articles selected for publication in these volumes were specifically chosen to introduce readers to advanced topics, to emphasize interdisciplinary connections, and to stress future research directions. Volume I contains contributions from invited speakers; Volume II contains additional contributed papers. Members of the Canadian Mathematical Society may order at the AMS member price.
New Developments In The Theory And Application Of Dirichlet Forms
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Author : S. Albeverio
language : en
Publisher:
Release Date : 1990
New Developments In The Theory And Application Of Dirichlet Forms written by S. Albeverio and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with categories.
Topics In Mathematical Analysis
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Author : Paolo Ciatti
language : en
Publisher: World Scientific
Release Date : 2008-06-16
Topics In Mathematical Analysis written by Paolo Ciatti and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-06-16 with Mathematics categories.
This volume consists of a series of lecture notes on mathematical analysis. The contributors have been selected on the basis of both their outstanding scientific level and their clarity of exposition. Thus, the present collection is particularly suited to young researchers and graduate students. Through this volume, the editors intend to provide the reader with material otherwise difficult to find and written in a manner which is also accessible to nonexperts.