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Stochastic Cauchy Problems In Infinite Dimensions
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Book Synopsis Stochastic Cauchy Problems in Infinite Dimensions by : Irina V. Melnikova
Download or read book Stochastic Cauchy Problems in Infinite Dimensions written by Irina V. Melnikova and published by CRC Press. This book was released on 2018-09-03 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic Cauchy Problems in Infinite Dimensions: Generalized and Regularized Solutions presents stochastic differential equations for random processes with values in Hilbert spaces. Accessible to non-specialists, the book explores how modern semi-group and distribution methods relate to the methods of infinite-dimensional stochastic analysis. It also shows how the idea of regularization in a broad sense pervades all these methods and is useful for numerical realization and applications of the theory. The book presents generalized solutions to the Cauchy problem in its initial form with white noise processes in spaces of distributions. It also covers the "classical" approach to stochastic problems involving the solution of corresponding integral equations. The first part of the text gives a self-contained introduction to modern semi-group and abstract distribution methods for solving the homogeneous (deterministic) Cauchy problem. In the second part, the author solves stochastic problems using semi-group and distribution methods as well as the methods of infinite-dimensional stochastic analysis.
Book Synopsis Stochastic Cauchy Problems in Infinite Dimensions by : Irina V. Melnikova
Download or read book Stochastic Cauchy Problems in Infinite Dimensions written by Irina V. Melnikova and published by CRC Press. This book was released on 2016-04-27 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic Cauchy Problems in Infinite Dimensions: Generalized and Regularized Solutions presents stochastic differential equations for random processes with values in Hilbert spaces. Accessible to non-specialists, the book explores how modern semi-group and distribution methods relate to the methods of infinite-dimensional stochastic analysis. It also shows how the idea of regularization in a broad sense pervades all these methods and is useful for numerical realization and applications of the theory. The book presents generalized solutions to the Cauchy problem in its initial form with white noise processes in spaces of distributions. It also covers the "classical" approach to stochastic problems involving the solution of corresponding integral equations. The first part of the text gives a self-contained introduction to modern semi-group and abstract distribution methods for solving the homogeneous (deterministic) Cauchy problem. In the second part, the author solves stochastic problems using semi-group and distribution methods as well as the methods of infinite-dimensional stochastic analysis.
Book Synopsis Stochastic Differential Equations in Infinite Dimensions by : Leszek Gawarecki
Download or read book Stochastic Differential Equations in Infinite Dimensions written by Leszek Gawarecki and published by Springer Science & Business Media. This book was released on 2010-11-29 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: The systematic study of existence, uniqueness, and properties of solutions to stochastic differential equations in infinite dimensions arising from practical problems characterizes this volume that is intended for graduate students and for pure and applied mathematicians, physicists, engineers, professionals working with mathematical models of finance. Major methods include compactness, coercivity, monotonicity, in a variety of set-ups. The authors emphasize the fundamental work of Gikhman and Skorokhod on the existence and uniqueness of solutions to stochastic differential equations and present its extension to infinite dimension. They also generalize the work of Khasminskii on stability and stationary distributions of solutions. New results, applications, and examples of stochastic partial differential equations are included. This clear and detailed presentation gives the basics of the infinite dimensional version of the classic books of Gikhman and Skorokhod and of Khasminskii in one concise volume that covers the main topics in infinite dimensional stochastic PDE’s. By appropriate selection of material, the volume can be adapted for a 1- or 2-semester course, and can prepare the reader for research in this rapidly expanding area.
Book Synopsis New Trends in Analysis and Interdisciplinary Applications by : Pei Dang
Download or read book New Trends in Analysis and Interdisciplinary Applications written by Pei Dang and published by Birkhäuser. This book was released on 2017-04-18 with total page 615 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a collection of papers from the 10th ISAAC Congress 2015, held in Macau, China. The papers, prepared by respected international experts, address recent results in Mathematics, with a special focus on Analysis. By structuring the content according to the various mathematical topics, the volume offers specialists and non-specialists alike an excellent source of information on the state-of-the-art in Mathematical Analysis and its interdisciplinary applications.
Book Synopsis Current Trends in Analysis and Its Applications by : Vladimir V. Mityushev
Download or read book Current Trends in Analysis and Its Applications written by Vladimir V. Mityushev and published by Birkhäuser. This book was released on 2015-02-04 with total page 842 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of papers from the 9th International ISAAC Congress held in 2013 in Kraków, Poland. The papers are devoted to recent results in mathematics, focused on analysis and a wide range of its applications. These include up-to-date findings of the following topics: - Differential Equations: Complex and Functional Analytic Methods - Nonlinear PDE - Qualitative Properties of Evolution Models - Differential and Difference Equations - Toeplitz Operators - Wavelet Theory - Topological and Geometrical Methods of Analysis - Queueing Theory and Performance Evaluation of Computer Networks - Clifford and Quaternion Analysis - Fixed Point Theory - M-Frame Constructions - Spaces of Differentiable Functions of Several Real Variables Generalized Functions - Analytic Methods in Complex Geometry - Topological and Geometrical Methods of Analysis - Integral Transforms and Reproducing Kernels - Didactical Approaches to Mathematical Thinking Their wide applications in biomathematics, mechanics, queueing models, scattering, geomechanics etc. are presented in a concise, but comprehensible way, such that further ramifications and future directions can be immediately seen.
Book Synopsis Trotter-Kato Approximations of Stochastic Differential Equations in Infinite Dimensions and Applications by : T. E. Govindan
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:
Book Synopsis Stochastic Equations in Infinite Dimensions by : Da Prato Guiseppe
Download or read book Stochastic Equations in Infinite Dimensions written by Da Prato Guiseppe and published by . This book was released on 2013-11-21 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to give a systematic and self-contained presentation of 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 Ito and Gikham 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 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. The book ends with a comprehensive bibliography that will contribute to the book's value for all working in stochastic differential equations."
Book Synopsis Stochastic Optimal Control in Infinite Dimension by : Giorgio Fabbri
Download or read book Stochastic Optimal Control in Infinite Dimension written by Giorgio Fabbri and published by Springer. This book was released on 2017-06-22 with total page 928 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing an introduction to stochastic optimal control in infinite dimension, this book gives a complete account of the theory of second-order HJB equations in infinite-dimensional Hilbert spaces, focusing on its applicability to associated stochastic optimal control problems. It features a general introduction to optimal stochastic control, including basic results (e.g. the dynamic programming principle) with proofs, and provides examples of applications. A complete and up-to-date exposition of the existing theory of viscosity solutions and regular solutions of second-order HJB equations in Hilbert spaces is given, together with an extensive survey of other methods, with a full bibliography. In particular, Chapter 6, written by M. Fuhrman and G. Tessitore, surveys the theory of regular solutions of HJB equations arising in infinite-dimensional stochastic control, via BSDEs. The book is of interest to both pure and applied researchers working in the control theory of stochastic PDEs, and in PDEs in infinite dimension. Readers from other fields who want to learn the basic theory will also find it useful. The prerequisites are: standard functional analysis, the theory of semigroups of operators and its use in the study of PDEs, some knowledge of the dynamic programming approach to stochastic optimal control problems in finite dimension, and the basics of stochastic analysis and stochastic equations in infinite-dimensional spaces.
Book Synopsis New Prospects in Direct, Inverse and Control Problems for Evolution Equations by : Angelo Favini
Download or read book New Prospects in Direct, Inverse and Control Problems for Evolution Equations written by Angelo Favini and published by Springer. This book was released on 2014-11-27 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, based on a selection of talks given at a dedicated meeting in Cortona, Italy, in June 2013, shows the high degree of interaction between a number of fields related to applied sciences. Applied sciences consider situations in which the evolution of a given system over time is observed, and the related models can be formulated in terms of evolution equations (EEs). These equations have been studied intensively in theoretical research and are the source of an enormous number of applications. In this volume, particular attention is given to direct, inverse and control problems for EEs. The book provides an updated overview of the field, revealing its richness and vitality.
Book Synopsis Seminar on Stochastic Analysis, Random Fields and Applications V by : Robert Dalang
Download or read book Seminar on Stochastic Analysis, Random Fields and Applications V written by Robert Dalang and published by Springer Science & Business Media. This book was released on 2008-03-12 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains refereed research or review papers presented at the 5th Seminar on Stochastic Processes, Random Fields and Applications, which took place at the Centro Stefano Franscini (Monte Verità) in Ascona, Switzerland, from May 29 to June 3, 2004. The seminar focused mainly on stochastic partial differential equations, stochastic models in mathematical physics, and financial engineering.
Book Synopsis Stochastic Equations in Infinite Dimensions by : Giuseppe Da Prato
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.
Book Synopsis Recent Advances in Operator Theory and Related Topics by : Laszlo Kerchy
Download or read book Recent Advances in Operator Theory and Related Topics written by Laszlo Kerchy and published by Birkhäuser. This book was released on 2012-12-06 with total page 719 pages. Available in PDF, EPUB and Kindle. Book excerpt: These 35 refereed articles report on recent and original results in various areas of operator theory and connected fields, many of them strongly related to contributions of Sz.-Nagy. The scientific part of the book is preceeded by fifty pages of biographical material, including several photos.
Book Synopsis Recent Developments in Infinite-Dimensional Analysis and Quantum Probability by : Luigi Accardi
Download or read book Recent Developments in Infinite-Dimensional Analysis and Quantum Probability written by Luigi Accardi and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent Developments in Infinite-Dimensional Analysis and Quantum Probability is dedicated to Professor Takeyuki Hida on the occasion of his 70th birthday. The book is more than a collection of articles. In fact, in it the reader will find a consistent editorial work, devoted to attempting to obtain a unitary picture from the different contributions and to give a comprehensive account of important recent developments in contemporary white noise analysis and some of its applications. For this reason, not only the latest results, but also motivations, explanations and connections with previous work have been included. The wealth of applications, from number theory to signal processing, from optimal filtering to information theory, from the statistics of stationary flows to quantum cable equations, show the power of white noise analysis as a tool. Beyond these, the authors emphasize its connections with practically all branches of contemporary probability, including stochastic geometry, the structure theory of stationary Gaussian processes, Neumann boundary value problems, and large deviations.
Book Synopsis Semigroups of Operators -Theory and Applications by : Jacek Banasiak
Download or read book Semigroups of Operators -Theory and Applications written by Jacek Banasiak and published by Springer. This book was released on 2014-11-20 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many results, both from semi group theory itself and from the applied sciences, are phrased in discipline-specific languages and hence are hardly known to a broader community. This volume contains a selection of lectures presented at a conference that was organised as a forum for all mathematicians using semi group theory to learn what is happening outside their own field of research. The collection will help to establish a number of new links between various sub-disciplines of semigroup theory, stochastic processes, differential equations and the applied fields. The theory of semigroups of operators is a well-developed branch of functional analysis. Its foundations were laid at the beginning of the 20th century, while the fundamental generation theorem of Hille and Yosida dates back to the forties. The theory was, from the very beginning, designed as a universal language for partial differential equations and stochastic processes, but at the same time it started to live as an independent branch of operator theory. Nowadays, it still has the same distinctive flavour: it develops rapidly by posing new ‘internal’ questions and in answering them, discovering new methods that can be used in applications. On the other hand, it is influenced by questions from PDEs and stochastic processes as well as from applied sciences such as mathematical biology and optimal control, and thus it continually gathers a new momentum. Researchers and postgraduate students working in operator theory, partial differential equations, probability and stochastic processes, analytical methods in biology and other natural sciences, optimization and optimal control will find this volume useful.
Book Synopsis A Minicourse on Stochastic Partial Differential Equations by : Robert C. Dalang
Download or read book A Minicourse on Stochastic Partial Differential Equations written by Robert C. Dalang and published by Springer Science & Business Media. This book was released on 2009 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: This title contains lectures that offer an introduction to modern topics in stochastic partial differential equations and bring together experts whose research is centered on the interface between Gaussian analysis, stochastic analysis, and stochastic PDEs.
Book Synopsis Stochastic Differential Equations in Infinite Dimensional Spaces by : G. Kallianpur
Download or read book Stochastic Differential Equations in Infinite Dimensional Spaces written by G. Kallianpur and published by IMS. This book was released on 1995 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Nonlinear Analysis and Applications by : V. Lakshmikantham
Download or read book Nonlinear Analysis and Applications written by V. Lakshmikantham and published by Springer Science & Business Media. This book was released on 2003 with total page 618 pages. Available in PDF, EPUB and Kindle. Book excerpt:
