Invariant Measures For Stochastic Nonlinear Schr Dinger Equations
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Invariant Measures For Stochastic Nonlinear Schr Dinger Equations
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Author : Jialin Hong
language : en
Publisher: Springer Nature
Release Date : 2019-08-22
Invariant Measures For Stochastic Nonlinear Schr Dinger Equations written by Jialin Hong and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-22 with Mathematics categories.
This book provides some recent advance in the study of stochastic nonlinear Schrödinger equations and their numerical approximations, including the well-posedness, ergodicity, symplecticity and multi-symplecticity. It gives an accessible overview of the existence and uniqueness of invariant measures for stochastic differential equations, introduces geometric structures including symplecticity and (conformal) multi-symplecticity for nonlinear Schrödinger equations and their numerical approximations, and studies the properties and convergence errors of numerical methods for stochastic nonlinear Schrödinger equations. This book will appeal to researchers who are interested in numerical analysis, stochastic analysis, ergodic theory, partial differential equation theory, etc.
Stochastic Dynamics
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Author : Hans Crauel
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-14
Stochastic Dynamics written by Hans Crauel 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 2007-12-14 with Mathematics categories.
Focusing on the mathematical description of stochastic dynamics in discrete as well as in continuous time, this book investigates such dynamical phenomena as perturbations, bifurcations and chaos. It also introduces new ideas for the exploration of infinite dimensional systems, in particular stochastic partial differential equations. Example applications are presented from biology, chemistry and engineering, while describing numerical treatments of stochastic systems.
Stochastics In Finite And Infinite Dimensions
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Author : Takeyuki Hida
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Stochastics In Finite And Infinite Dimensions written by Takeyuki Hida 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.
During the last fifty years, Gopinath Kallianpur has made extensive and significant contributions to diverse areas of probability and statistics, including stochastic finance, Fisher consistent estimation, non-linear prediction and filtering problems, zero-one laws for Gaussian processes and reproducing kernel Hilbert space theory, and stochastic differential equations in infinite dimensions. To honor Kallianpur's pioneering work and scholarly achievements, a number of leading experts have written research articles highlighting progress and new directions of research in these and related areas. This commemorative volume, dedicated to Kallianpur on the occasion of his seventy-fifth birthday, will pay tribute to his multi-faceted achievements and to the deep insight and inspiration he has so graciously offered his students and colleagues throughout his career. Contributors to the volume: S. Aida, N. Asai, K. B. Athreya, R. N. Bhattacharya, A. Budhiraja, P. S. Chakraborty, P. Del Moral, R. Elliott, L. Gawarecki, D. Goswami, Y. Hu, J. Jacod, G. W. Johnson, L. Johnson, T. Koski, N. V. Krylov, I. Kubo, H.-H. Kuo, T. G. Kurtz, H. J. Kushner, V. Mandrekar, B. Margolius, R. Mikulevicius, I. Mitoma, H. Nagai, Y. Ogura, K. R. Parthasarathy, V. Perez-Abreu, E. Platen, B. V. Rao, B. Rozovskii, I. Shigekawa, K. B. Sinha, P. Sundar, M. Tomisaki, M. Tsuchiya, C. Tudor, W. A. Woycynski, J. Xiong.
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.
Asymptotic Analysis For Functional Stochastic Differential Equations
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Author : Jianhai Bao
language : en
Publisher: Springer
Release Date : 2016-11-19
Asymptotic Analysis For Functional Stochastic Differential Equations written by Jianhai Bao and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-19 with Mathematics categories.
This brief treats dynamical systems that involve delays and random disturbances. The study is motivated by a wide variety of systems in real life in which random noise has to be taken into consideration and the effect of delays cannot be ignored. Concentrating on such systems that are described by functional stochastic differential equations, this work focuses on the study of large time behavior, in particular, ergodicity.This brief is written for probabilists, applied mathematicians, engineers, and scientists who need to use delay systems and functional stochastic differential equations in their work. Selected topics from the brief can also be used in a graduate level topics course in probability and stochastic processes.
Stochastic Partial Differential Equations And Applications Vii
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Author : Giuseppe Da Prato
language : en
Publisher: CRC Press
Release Date : 2005-10-12
Stochastic Partial Differential Equations And Applications Vii written by Giuseppe Da Prato and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-10-12 with Mathematics categories.
Stochastic Partial Differential Equations and Applications gives an overview of current state-of-the-art stochastic PDEs in several fields, such as filtering theory, stochastic quantization, quantum probability, and mathematical finance. Featuring contributions from leading expert participants at an international conference on the subject, this boo
Stochastic Partial Differential Equations And Applications
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Author : Giuseppe Da Prato
language : en
Publisher: CRC Press
Release Date : 2002-04-05
Stochastic Partial Differential Equations And Applications written by Giuseppe Da Prato and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-04-05 with Mathematics categories.
Based on the proceedings of the International Conference on Stochastic Partial Differential Equations and Applications-V held in Trento, Italy, this illuminating reference presents applications in filtering theory, stochastic quantization, quantum probability, and mathematical finance and identifies paths for future research in the field. Stochastic Partial Differential Equations and Applications analyzes recent developments in the study of quantum random fields, control theory, white noise, and fluid dynamics. It presents precise conditions for nontrivial and well-defined scattering, new Gaussian noise terms, models depicting the asymptotic behavior of evolution equations, and solutions to filtering dilemmas in signal processing. With contributions from more than 40 leading experts in the field, Stochastic Partial Differential Equations and Applications is an excellent resource for pure and applied mathematicians; numerical analysts; mathematical physicists; geometers; economists; probabilists; computer scientists; control, electrical, and electronics engineers; and upper-level undergraduate and graduate students in these disciplines.
Almost Sure Scattering For The One Dimensional Nonlinear Schr Dinger Equation
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Author : Nicolas Burq
language : en
Publisher: American Mathematical Society
Release Date : 2024-05-15
Almost Sure Scattering For The One Dimensional Nonlinear Schr Dinger Equation written by Nicolas Burq and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-05-15 with Mathematics categories.
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Transformation Groups And Invariant Measures
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Author : A B Kharazishvili
language : en
Publisher: World Scientific
Release Date : 1998-10-05
Transformation Groups And Invariant Measures written by A B Kharazishvili and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-10-05 with Mathematics categories.
This book is devoted to some topics of the general theory of invariant and quasi-invariant measures. Such measures are usually defined on various σ-algebras of subsets of spaces equipped with transformation groups, and there are close relationships between purely algebraic properties of these groups and the corresponding properties of invariant (quasi-invariant) measures. The main goal of the book is to investigate several aspects of those relationships (primarily from the set-theoretical point of view). Also of interest are the properties of some natural classes of sets, important from the viewpoint of the theory of invariant (quasi-invariant) measures. Contents:Some Properties of Transformation GroupsQuasiinvariant and Invariant MeasuresSome Examples and ConstructionsNonmeasurable Sets with Respect to Quasiinvariant and Invariant MeasuresSmall Sets with Respect to Quasiinvariant MeasuresAlmost Invariant SetsSome Invariant σ-Ideals and σ-AlgebrasDensity Points and Invariant Extensions of Lebesgue MeasureThe Uniqueness of Lebesgue and Borel MeasuresQuasiinvariant Borel Measures on Standard Groups Readership: Pure mathematicians. Keywords:Transformation Group;Invariant Measure;Quasi-Invariant Measure;Absolutely Negligible Set;Absolutely Nonmeasurable Set;Extension of Measure;Haar Measure;Lebesgue Measure;Uniqueness Property for Measures;Steinhaus Property;Metrical Transitivity;Standard Group;Measurable Cardinal
Stochastic Analysis And Diffusion Processes
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Author : Gopinath Kallianpur
language : en
Publisher: OUP Oxford
Release Date : 2014-01-09
Stochastic Analysis And Diffusion Processes written by Gopinath Kallianpur and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-09 with Mathematics categories.
Stochastic Analysis and Diffusion Processes presents a simple, mathematical introduction to Stochastic Calculus and its applications. The book builds the basic theory and offers a careful account of important research directions in Stochastic Analysis. The breadth and power of Stochastic Analysis, and probabilistic behavior of diffusion processes are told without compromising on the mathematical details. Starting with the construction of stochastic processes, the book introduces Brownian motion and martingales. The book proceeds to construct stochastic integrals, establish the Itô formula, and discuss its applications. Next, attention is focused on stochastic differential equations (SDEs) which arise in modeling physical phenomena, perturbed by random forces. Diffusion processes are solutions of SDEs and form the main theme of this book. The Stroock-Varadhan martingale problem, the connection between diffusion processes and partial differential equations, Gaussian solutions of SDEs, and Markov processes with jumps are presented in successive chapters. The book culminates with a careful treatment of important research topics such as invariant measures, ergodic behavior, and large deviation principle for diffusions. Examples are given throughout the book to illustrate concepts and results. In addition, exercises are given at the end of each chapter that will help the reader to understand the concepts better. The book is written for graduate students, young researchers and applied scientists who are interested in stochastic processes and their applications. The reader is assumed to be familiar with probability theory at graduate level. The book can be used as a text for a graduate course on Stochastic Analysis.