Download or read book Uniqueness for Stochastic Evolution Equations in Banach Spaces written by Martin Ondreját and published by . This book was released on 2004 with total page 72 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Measure Valued Solutions for Nonlinear Evolution Equations on Banach Spaces and Their Optimal Control written by N. U. Ahmed and published by Springer Nature. This book was released on 2023-09-12 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers the first comprehensive presentation of measure-valued solutions for nonlinear deterministic and stochastic evolution equations on infinite dimensional Banach spaces. Unlike traditional solutions, measure-valued solutions allow for a much broader class of abstract evolution equations to be addressed, providing a broader approach. The book presents extensive results on the existence of measure-valued solutions for differential equations that have no solutions in the usual sense. It covers a range of topics, including evolution equations with continuous/discontinuous vector fields, neutral evolution equations subject to vector measures as impulsive forces, stochastic evolution equations, and optimal control of evolution equations. The optimal control problems considered cover the existence of solutions, necessary conditions of optimality, and more, significantly complementing the existing literature. This book will be of great interest to researchers in functional analysis, partial differential equations, dynamic systems and their optimal control, and their applications, advancing previous research and providing a foundation for further exploration of the field.

Download or read book Evolution Equations in Scales of Banach Spaces written by Oliver Caps and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides a new functional-analytic approach to evolution equations by considering the abstract Cauchy problem in a scale of Banach spaces. Conditions are proved characterizing well-posedness of the linear, time-dependent Cauchy problem in scales of Banach spaces and implying local existence, uniqueness, and regularity of solutions of the quasilinear Cauchy problem. Many applications illustrate the generality of the approach. In particular, using the Fefferman-Phong inequality unifying results on parabolic and hyperbolic equations generalizing classical ones and a unified treatment of Navier-Stokes and Euler equations is described. Assuming only basic knowledge in analysis and functional analysis the book provides all mathematical tools and is aimed for students, graduates, researchers, and lecturers.

Download or read book Stochastic Evolution Equations written by Wilfried Grecksch and published by De Gruyter Akademie Forschung. This book was released on 1995 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors give a self-contained exposition of the theory of stochastic evolution equations. Elements of infinite dimensional analysis, martingale theory in Hilbert spaces, stochastic integrals, stochastic convolutions are applied. Existence and uniqueness theorems for stochastic evolution equations in Hilbert spaces in the sense of the semigroup theory, the theory of evolution operators, and monotonous operators in rigged Hilbert spaces are discussed. Relationships between the different concepts are demonstrated. The results are used to concrete stochastic partial differential equations like parabolic and hyperbolic Ito equations and random constitutive equations of elastic viscoplastic materials. Furthermore, stochastic evolution equations in rigged Hilbert spaces are approximated by time discretization methods.

Download or read book Stochastic Equations in Infinite Dimensions written by Giuseppe Da Prato and published by Cambridge University Press. This book was released on 2014-04-17 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: Updates in this second edition include two brand new chapters and an even more comprehensive bibliography.

Download or read book Stochastic Differential Equations written by Peter H. Baxendale and published by World Scientific. This book was released on 2007 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of 15 articles written by experts in stochastic analysis. The first paper in the volume, Stochastic Evolution Equations by N V Krylov and B L Rozovskii, was originally published in Russian in 1979. After more than a quarter-century, this paper remains a standard reference in the field of stochastic partial differential equations (SPDEs) and continues to attract the attention of mathematicians of all generations. Together with a short but thorough introduction to SPDEs, it presents a number of optimal, and essentially unimprovable, results about solvability for a large class of both linear and non-linear equations. The other papers in this volume were specially written for the occasion of Prof RozovskiiOCOs 60th birthday. They tackle a wide range of topics in the theory and applications of stochastic differential equations, both ordinary and with partial derivatives."

Download or read book Stochastic Equations in Infinite Dimensions written by Giuseppe Da Prato and published by Cambridge University Press. This book was released on 2014-04-17 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: Now in its second edition, this book gives a systematic and self-contained presentation of basic results on stochastic evolution equations in infinite dimensional, typically Hilbert and Banach, spaces. In the first part the authors give a self-contained exposition of the basic properties of probability measure on separable Banach and Hilbert spaces, as required later; they assume a reasonable background in probability theory and finite dimensional stochastic processes. The second part is devoted to the existence and uniqueness of solutions of a general stochastic evolution equation, and the third concerns the qualitative properties of those solutions. Appendices gather together background results from analysis that are otherwise hard to find under one roof. This revised edition includes two brand new chapters surveying recent developments in the area and an even more comprehensive bibliography, making this book an essential and up-to-date resource for all those working in stochastic differential equations.

Download or read book Stochastic Differential Equations Theory And Applications A Volume In Honor Of Professor Boris L Rozovskii written by Peter H Baxendale and published by World Scientific. This book was released on 2007-04-19 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of 15 articles written by experts in stochastic analysis. The first paper in the volume, Stochastic Evolution Equations by N V Krylov and B L Rozovskii, was originally published in Russian in 1979. After more than a quarter-century, this paper remains a standard reference in the field of stochastic partial differential equations (SPDEs) and continues to attract the attention of mathematicians of all generations. Together with a short but thorough introduction to SPDEs, it presents a number of optimal, and essentially unimprovable, results about solvability for a large class of both linear and non-linear equations.The other papers in this volume were specially written for the occasion of Prof Rozovskii's 60th birthday. They tackle a wide range of topics in the theory and applications of stochastic differential equations, both ordinary and with partial derivatives.

Download or read book Stochastic Equations in Infinite Dimensions Second Edition written by Giuseppe Da Prato and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Stochastic Equations in Infinite Dimensions written by Guiseppe Da Prato and published by Cambridge University Press. This book was released on 2008-02-04 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to give a systematic and self-contained presentation of the basic results on stochastic evolution equations in infinite dimensional, typically Hilbert and Banach, spaces. These are a generalization of stochastic differential equations as introduced by Itô and Gikhman that occur, for instance, when describing random phenomena that crop up in science and engineering, as well as in the study of differential equations. The book is divided into three parts. In the first the authors give a self-contained exposition of the basic properties of probability measures on separable Banach and Hilbert spaces, as required later; they assume a reasonable background in probability theory and finite dimensional stochastic processes. The second part is devoted to the existence and uniqueness of solutions of a general stochastic evolution equation, and the third concerns the qualitative properties of those solutions. Appendices gather together background results from analysis that are otherwise hard to find under one roof.

Download or read book Stochastic Partial Differential Equations written by Pao-Liu Chow and published by CRC Press. This book was released on 2014-12-10 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explore Theory and Techniques to Solve Physical, Biological, and Financial Problems Since the first edition was published, there has been a surge of interest in stochastic partial differential equations (PDEs) driven by the Levy type of noise. Stochastic Partial Differential Equations, Second Edition incorporates these recent developments and impro

Download or read book Stochastic Partial Differential Equations with L vy Noise written by S. Peszat and published by Cambridge University Press. This book was released on 2007-10-11 with total page 45 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprehensive monograph by two leading international experts; includes applications to statistical and fluid mechanics and to finance.

Download or read book Dynamics of Stochastic Evolution Equations in Banach Spaces written by Alexandra-Aurelia Neamţu and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book A Concise Guide To Semigroups And Evolution Equations written by Aldo Belleni-morante and published by World Scientific. This book was released on 1994-05-18 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a simple and concise introduction to the theory of semigroups and evolution equations, both in the linear and in the semilinear case. The subject is presented by a discussion of two standard boundary value problems (from particle transport theory and from population theory), and by showing how such problems can be rewritten as evolution problems in suitable Banach spaces.Each section of the book is completed by some notes, where the relevant notions of functional analysis are explained. Some other definitions and theorems of functional analysis are discussed in the Appendices (so that the only prerequisites to read the book are classical differential and integral calculus).

Download or read book Evolution Equations Semigroups and Functional Analysis written by Brunello Terreni and published by Springer Science & Business Media. This book was released on 2002 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: Brunello Terreni (1953-2000) was a researcher and teacher with vision and dedication. The present volume is dedicated to the memory of Brunello Terreni. His mathematical interests are reflected in 20 expository articles written by distinguished mathematicians. The unifying theme of the articles is "evolution equations and functional analysis", which is presented in various and diverse forms: parabolic equations, semigroups, stochastic evolution, optimal control, existence, uniqueness and regularity of solutions, inverse problems as well as applications. Contributors: P. Acquistapace, V. Barbu, A. Briani, L. Boccardo, P. Colli Franzone, G. Da Prato, D. Donatelli, A. Favini, M. Fuhrmann, M. Grasselli, R. Illner, H. Koch, R. Labbas, H. Lange, I. Lasiecka, A. Lorenzi, A. Lunardi, P. Marcati, R. Nagel, G. Nickel, V. Pata, M. M. Porzio, B. Ruf, G. Savaré, R. Schnaubelt, E. Sinestrari, H. Tanabe, H. Teismann, E. Terraneo, R. Triggiani, A. Yagi

Download or read book Trotter Kato Approximations of Stochastic Differential Equations in Infinite Dimensions and Applications written by T. E. Govindan and published by Springer Nature. This book was released on with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Introduction to Stochastic Partial Differential Equations written by István Gyöngy and published by Springer. This book was released on 2011 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: The $L_2$-theory of parabolic SPDEs is presented in this book. The development of the theory of SPDEs is motivated by problems arising in practice surrounding the numerical calculations of nonlinear filters for partially observed diffusion processes. To address these questions, the dependence of SPDEs on the driving semimartingales is investigated and new results on their numerical approximations are also given. In contrast to previous expositions, SPDEs driven by random measures and discontinuous semimartingales are also considered, and the theory of SPDEs driven by Levy processes are included as special cases. The author introduces a more general theory of SPDEs developing the theory of stochastic evolution equations in Banach spaces. He presents applications to large classes of linear and nonlinear SPDEs and , in particular, he developes a theory of SPDEs with unbounded coefficients in weighted Sobolev spaces. In this unique book regularity properties of the solutions are obtained via new results on dependence of the solutions on parameters, and existence and uniqueness theorems for parabolic SPDEs on smooth domains of $R^d$ are proven. Furthermore, the present book makes the theory more accessible for beginners, because initial linear parabolic SPDEs on the whole $R^d$ are considered, and the main existence and uniqueness results are obtained by elementary methods while exercises and applications are also provided