Approximation Of Stochastic Invariant Manifolds
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Approximation Of Stochastic Invariant Manifolds
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Author : Mickaël D. Chekroun
language : en
Publisher: Springer
Release Date : 2014-12-20
Approximation Of Stochastic Invariant Manifolds written by Mickaël D. Chekroun and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-20 with Mathematics categories.
This first volume is concerned with the analytic derivation of explicit formulas for the leading-order Taylor approximations of (local) stochastic invariant manifolds associated with a broad class of nonlinear stochastic partial differential equations. These approximations take the form of Lyapunov-Perron integrals, which are further characterized in Volume II as pullback limits associated with some partially coupled backward-forward systems. This pullback characterization provides a useful interpretation of the corresponding approximating manifolds and leads to a simple framework that unifies some other approximation approaches in the literature. A self-contained survey is also included on the existence and attraction of one-parameter families of stochastic invariant manifolds, from the point of view of the theory of random dynamical systems.
Invariant Manifolds For Stochastic Pde With Fractional Brownian Motion
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Author : Alberto Ohashi
language : en
Publisher:
Release Date : 2007
Invariant Manifolds For Stochastic Pde With Fractional Brownian Motion written by Alberto Ohashi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with categories.
Stochastic Parameterizing Manifolds And Non Markovian Reduced Equations
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Author : Mickaël D. Chekroun
language : en
Publisher: Springer
Release Date : 2014-12-23
Stochastic Parameterizing Manifolds And Non Markovian Reduced Equations written by Mickaël D. Chekroun and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-23 with Mathematics categories.
In this second volume, a general approach is developed to provide approximate parameterizations of the "small" scales by the "large" ones for a broad class of stochastic partial differential equations (SPDEs). This is accomplished via the concept of parameterizing manifolds (PMs), which are stochastic manifolds that improve, for a given realization of the noise, in mean square error the partial knowledge of the full SPDE solution when compared to its projection onto some resolved modes. Backward-forward systems are designed to give access to such PMs in practice. The key idea consists of representing the modes with high wave numbers as a pullback limit depending on the time-history of the modes with low wave numbers. Non-Markovian stochastic reduced systems are then derived based on such a PM approach. The reduced systems take the form of stochastic differential equations involving random coefficients that convey memory effects. The theory is illustrated on a stochastic Burgers-type equation.
Stochastic Pdes And Modelling Of Multiscale Complex System
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Author : Wang Wei
language : en
Publisher: World Scientific
Release Date : 2019-05-07
Stochastic Pdes And Modelling Of Multiscale Complex System written by Wang Wei and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-07 with Mathematics categories.
This volume is devoted to original research results and survey articles reviewing recent developments in reduction for stochastic PDEs with multiscale as well as application to science and technology, and to present some future research direction. This volume includes a dozen chapters by leading experts in the area, with a broad audience in mind. It should be accessible to graduate students, junior researchers and other professionals who are interested in the subject. We also take this opportunity to celebrate the contributions of Professor Anthony J Roberts, an internationally leading figure on the occasion of his 60th years birthday in 2017.
Invariant Manifolds In Discrete And Continuous Dynamical Systems
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Author : Kaspar Nipp
language : en
Publisher:
Release Date : 2013
Invariant Manifolds In Discrete And Continuous Dynamical Systems written by Kaspar Nipp and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Banach spaces categories.
In this book, dynamical systems are investigated from a geometric viewpoint. Admitting an invariant manifold is a strong geometric property of a dynamical system. This text presents rigorous results on invariant manifolds and gives examples of possible applications. In the first part, discrete dynamical systems in Banach spaces are considered. Results on the existence and smoothness of attractive and repulsive invariant manifolds are derived. In addition, perturbations and approximations of the manifolds and the foliation of the adjacent space are treated. In the second part, analogous results for continuous dynamical systems in finite dimensions are established. In the third part, the theory developed is applied to problems in numerical analysis and to singularly perturbed systems of ordinary differential equations. The mathematical approach is based on the so-called graph transform, already used by Hadamard in 1901. The aim is to establish invariant manifold results in a simple setting that provides quantitative estimates. The book is targeted at researchers in the field of dynamical systems interested in precise theorems that are easy to apply. The application part might also serve as an underlying text for a student seminar in mathematics. A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.
Lyapunov Exponents And Invariant Manifolds For Random Dynamical Systems In A Banach Space
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Author : Zeng Lian
language : en
Publisher: American Mathematical Soc.
Release Date : 2010
Lyapunov Exponents And Invariant Manifolds For Random Dynamical Systems In A Banach Space written by Zeng Lian 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 2010 with Banach spaces categories.
The authors study the Lyapunov exponents and their associated invariant subspaces for infinite dimensional random dynamical systems in a Banach space, which are generated by, for example, stochastic or random partial differential equations. The authors prove a multiplicative ergodic theorem and then use this theorem to establish the stable and unstable manifold theorem for nonuniformly hyperbolic random invariant sets.
Smooth Invariant Manifolds And Normal Forms
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Author : Alexander Kopanskii
language : en
Publisher: World Scientific
Release Date : 1994-12-22
Smooth Invariant Manifolds And Normal Forms written by Alexander Kopanskii and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-12-22 with Science categories.
This book deals with the qualitative theory of dynamical systems and is devoted to the study of flows and cascades in the vicinity of a smooth invariant manifold. Its main purpose is to present, as completely as possible, the basic results concerning the existence of stable and unstable local manifolds and the recent advancements in the theory of finitely smooth normal forms of vector fields and diffeomorphisms in the vicinity of a rest point and a periodic trajectory. A summary of the results obtained so far in the investigation of dynamical systems near an arbitrary invariant submanifold is also given.
Invariant Manifolds
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Author : M.W. Hirsch
language : en
Publisher: Springer
Release Date : 2006-11-15
Invariant Manifolds written by M.W. Hirsch 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.
Infinite Dimensional And Finite Dimensional Stochastic Equations And Applications In Physics
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Author : Wilfried Grecksch
language : en
Publisher: World Scientific
Release Date : 2020-04-22
Infinite Dimensional And Finite Dimensional Stochastic Equations And Applications In Physics written by Wilfried Grecksch and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-22 with Science categories.
This volume contains survey articles on various aspects of stochastic partial differential equations (SPDEs) and their applications in stochastic control theory and in physics.The topics presented in this volume are:This book is intended not only for graduate students in mathematics or physics, but also for mathematicians, mathematical physicists, theoretical physicists, and science researchers interested in the physical applications of the theory of stochastic processes.
Extremes And Recurrence In Dynamical Systems
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Author : Valerio Lucarini
language : en
Publisher: John Wiley & Sons
Release Date : 2016-04-04
Extremes And Recurrence In Dynamical Systems written by Valerio Lucarini and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-04 with Mathematics categories.
Written by a team of international experts, Extremes and Recurrence in Dynamical Systems presents a unique point of view on the mathematical theory of extremes and on its applications in the natural and social sciences. Featuring an interdisciplinary approach to new concepts in pure and applied mathematical research, the book skillfully combines the areas of statistical mechanics, probability theory, measure theory, dynamical systems, statistical inference, geophysics, and software application. Emphasizing the statistical mechanical point of view, the book introduces robust theoretical embedding for the application of extreme value theory in dynamical systems. Extremes and Recurrence in Dynamical Systems also features: • A careful examination of how a dynamical system can serve as a generator of stochastic processes • Discussions on the applications of statistical inference in the theoretical and heuristic use of extremes • Several examples of analysis of extremes in a physical and geophysical context • A final summary of the main results presented along with a guide to future research projects • An appendix with software in Matlab® programming language to help readers to develop further understanding of the presented concepts Extremes and Recurrence in Dynamical Systems is ideal for academics and practitioners in pure and applied mathematics, probability theory, statistics, chaos, theoretical and applied dynamical systems, statistical mechanics, geophysical fluid dynamics, geosciences and complexity science. VALERIO LUCARINI, PhD, is Professor of Theoretical Meteorology at the University of Hamburg, Germany and Professor of Statistical Mechanics at the University of Reading, UK. DAVIDE FARANDA, PhD, is Researcher at the Laboratoire des science du climat et de l’environnement, IPSL, CEA Saclay, Université Paris-Saclay, Gif-sur-Yvette, France. ANA CRISTINA GOMES MONTEIRO MOREIRA DE FREITAS, PhD, is Assistant Professor in the Faculty of Economics at the University of Porto, Portugal. JORGE MIGUEL MILHAZES DE FREITAS, PhD, is Assistant Professor in the Department of Mathematics of the Faculty of Sciences at the University of Porto, Portugal. MARK HOLLAND, PhD, is Senior Lecturer in Applied Mathematics in the College of Engineering, Mathematics and Physical Sciences at the University of Exeter, UK. TOBIAS KUNA, PhD, is Associate Professor in the Department of Mathematics and Statistics at the University of Reading, UK. MATTHEW NICOL, PhD, is Professor of Mathematics at the University of Houston, USA. MIKE TODD, PhD, is Lecturer in the School of Mathematics and Statistics at the University of St. Andrews, Scotland. SANDRO VAIENTI, PhD, is Professor of Mathematics at the University of Toulon and Researcher at the Centre de Physique Théorique, France.