Analysis For Diffusion Processes On Riemannian Manifolds
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Analysis For Diffusion Processes On Riemannian Manifolds
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Author : Feng-Yu Wang
language : en
Publisher: World Scientific
Release Date : 2014
Analysis For Diffusion Processes On Riemannian Manifolds written by Feng-Yu Wang and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with Mathematics categories.
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.
Stochastic Analysis On Manifolds
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Author : Elton P. Hsu
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
Stochastic Analysis On Manifolds written by Elton P. Hsu 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 2002 with Mathematics categories.
Mainly from the perspective of a probabilist, Hsu shows how stochastic analysis and differential geometry can work together for their mutual benefit. He writes for researchers and advanced graduate students with a firm foundation in basic euclidean stochastic analysis, and differential geometry. He does not include the exercises usual to such texts, but does provide proofs throughout that invite readers to test their understanding. Annotation copyrighted by Book News Inc., Portland, OR.
Stochastic Differential Equations On Manifolds
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Author : K. D. Elworthy
language : en
Publisher: Cambridge University Press
Release Date : 1982
Stochastic Differential Equations On Manifolds written by K. D. Elworthy and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with Manifolds (Mathematics). categories.
The aims of this book, originally published in 1982, are to give an understanding of the basic ideas concerning stochastic differential equations on manifolds and their solution flows, to examine the properties of Brownian motion on Riemannian manifolds when it is constructed using the stochiastic development and to indicate some of the uses of the theory. The author has included two appendices which summarise the manifold theory and differential geometry needed to follow the development; coordinate-free notation is used throughout. Moreover, the stochiastic integrals used are those which can be obtained from limits of the Riemann sums, thereby avoiding much of the technicalities of the general theory of processes and allowing the reader to get a quick grasp of the fundamental ideas of stochastic integration as they are needed for a variety of applications.
Analysis And Geometry Of Markov Diffusion Operators
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Author : Dominique Bakry
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-18
Analysis And Geometry Of Markov Diffusion Operators written by Dominique Bakry 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 2013-11-18 with Mathematics categories.
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.
On The Geometry Of Diffusion Operators And Stochastic Flows
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Author : K.D. Elworthy
language : en
Publisher: Springer
Release Date : 2007-01-05
On The Geometry Of Diffusion Operators And Stochastic Flows written by K.D. Elworthy and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-05 with Mathematics categories.
Stochastic differential equations, and Hoermander form representations of diffusion operators, can determine a linear connection associated to the underlying (sub)-Riemannian structure. This is systematically described, together with its invariants, and then exploited to discuss qualitative properties of stochastic flows, and analysis on path spaces of compact manifolds with diffusion measures. This should be useful to stochastic analysts, especially those with interests in stochastic flows, infinite dimensional analysis, or geometric analysis, and also to researchers in sub-Riemannian geometry. A basic background in differential geometry is assumed, but the construction of the connections is very direct and itself gives an intuitive and concrete introduction. Knowledge of stochastic analysis is also assumed for later chapters.
Harnack Inequalities For Stochastic Partial Differential Equations
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Author : Feng-Yu Wang
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-08-13
Harnack Inequalities For Stochastic Partial Differential Equations written by Feng-Yu Wang 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 2013-08-13 with Mathematics categories.
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.
Probability Towards 2000
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Author : L. Accardi
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Probability Towards 2000 written by L. Accardi 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.
Senior probabilists from around the world with widely differing specialities gave their visions of the state of their specialty, why they think it is important, and how they think it will develop in the new millenium. The volume includes papers given at a symposium at Columbia University in 1995, but papers from others not at the meeting were added to broaden the coverage of areas. All papers were refereed.
Comparison Theorems In Riemannian Geometry
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Author : Jeff Cheeger
language : en
Publisher: Newnes
Release Date : 1975
Comparison Theorems In Riemannian Geometry written by Jeff Cheeger and has been published by Newnes this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with Mathematics categories.
Open Quantum Systems
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Author : Dorothea Bahns
language : en
Publisher: Springer
Release Date : 2019-06-28
Open Quantum Systems written by Dorothea Bahns and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-28 with Mathematics categories.
This book presents four survey articles on various aspects of open quantum systems, specifically addressing quantum Markovian processes, Feller semigroups and nonequilibrium dynamics. The contributions are based on lectures given by distinguished experts at a summer school in Göttingen, Germany. 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.
Distribution Dependent Stochastic Differential Equations
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Author : Feng-yu Wang
language : en
Publisher: World Scientific
Release Date : 2024-09-26
Distribution Dependent Stochastic Differential Equations written by Feng-yu Wang and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-26 with Mathematics categories.
Corresponding to the link of Itô's stochastic differential equations (SDEs) and linear parabolic equations, distribution dependent SDEs (DDSDEs) characterize nonlinear Fokker-Planck equations. This type of SDEs is named after McKean-Vlasov due to the pioneering work of H P McKean (1966), where an expectation dependent SDE is proposed to characterize nonlinear PDEs for Maxwellian gas. Moreover, by using the propagation of chaos for Kac particle systems, weak solutions of DDSDEs are constructed as weak limits of mean field particle systems when the number of particles goes to infinity, so that DDSDEs are also called mean-field SDEs. To restrict a DDSDE in a domain, we consider the reflection boundary by following the line of A V Skorohod (1961).This book provides a self-contained account on singular SDEs and DDSDEs with or without reflection. It covers well-posedness and regularities for singular stochastic differential equations; well-posedness for singular reflected SDEs; well-posedness of singular DDSDEs; Harnack inequalities and derivative formulas for singular DDSDEs; long time behaviors for DDSDEs; DDSDEs with reflecting boundary; and killed DDSDEs.