Stochastic Cauchy Problems In Infinite Dimensions
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Stochastic Cauchy Problems In Infinite Dimensions
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Author : Irina V. Melnikova
language : en
Publisher: CRC Press
Release Date : 2016-02-22
Stochastic Cauchy Problems In Infinite Dimensions written by Irina V. Melnikova and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-22 with Mathematics categories.
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.
Trotter Kato Approximations Of Stochastic Differential Equations In Infinite Dimensions And Applications
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Author : T. E. Govindan
language : en
Publisher: Springer Nature
Release Date : 2024-07-01
Trotter Kato Approximations Of Stochastic Differential Equations In Infinite Dimensions And Applications written by T. E. Govindan and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-01 with Mathematics categories.
This is the first comprehensive book on Trotter-Kato approximations of stochastic differential equations (SDEs) in infinite dimensions and applications. This research monograph brings together the varied literature on this topic since 1985 when such a study was initiated. The author provides a clear and systematic introduction to the theory of Trotter-Kato approximations of SDEs and also presents its applications to practical topics such as stochastic stability and stochastic optimal control. The theory assimilated here is developed slowly and methodically in digestive pieces. The book begins with a motivational chapter introducing several different models that highlight the importance of the theory on abstract SDEs that will be considered in the subsequent chapters. The author next introduces the necessary mathematical background and then leads the reader into the main discussion of the monograph, namely, the Trotter-Kato approximations of many classes of SDEs in Hilbert spaces, Trotter-Kato approximations of SDEs in UMD Banach spaces and some of their applications. Most of the results presented in the main chapters appear for the first time in a book form. The monograph also contains many illustrative examples on stochastic partial differential equations and one in finance as an application of the Trotter-Kato formula. The key steps are included in all proofs which will help the reader to get a real insight into the theory of Trotter-Kato approximations and its use. This book is intended for researchers and graduate students in mathematics specializing in probability theory. It will also be useful to numerical analysts, engineers, physicists and practitioners who are interested in applying the theory of stochastic evolution equations. Since the approach is based mainly in semigroup theory, it is accessible to a wider audience including non-specialists in stochastic processes.
Seminar On Stochastic Analysis Random Fields And Applications V
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Author : Robert Dalang
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-03-12
Seminar On Stochastic Analysis Random Fields And Applications V written by Robert Dalang 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 2008-03-12 with Mathematics categories.
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.
New Prospects In Direct Inverse And Control Problems For Evolution Equations
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Author : Angelo Favini
language : en
Publisher: Springer
Release Date : 2014-11-27
New Prospects In Direct Inverse And Control Problems For Evolution Equations written by Angelo Favini and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-27 with Mathematics categories.
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.
New Trends In Analysis And Interdisciplinary Applications
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Author : Pei Dang
language : en
Publisher: Birkhäuser
Release Date : 2017-04-18
New Trends In Analysis And Interdisciplinary Applications written by Pei Dang and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-18 with Mathematics categories.
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.
Current Trends In Analysis And Its Applications
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Author : Vladimir V. Mityushev
language : en
Publisher: Birkhäuser
Release Date : 2015-02-04
Current Trends In Analysis And Its Applications written by Vladimir V. Mityushev and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-02-04 with Mathematics categories.
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.
Nonlinear Stochastic Problems
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Author : S. Bucy
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Nonlinear Stochastic Problems written by S. Bucy 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.
This volume corresponds to the invited lectures and advanced research papers presented at the NATD Advanced Study Institute on Nonlinear Stochastic Problems with emphasis on Identification, Signal Processing, Control and Nonlinear Filtering held in Algarve (Portugal), on May 1982. The book is a blend of theoretical issues, algorithmic implementation aspects, and application examples. In many areas of science and engineering, there are problems which are intrinsically nonlinear 3nd stochastic in nature. Clear examples arise in identification and mOdeling, signal processing, nonlinear filtering, stochastic and adaptive conLrol. The meeting was organized because it was felt that there is a need for discussion of the methods and philosophy underlying these different areas, and in order to communicate those approaches that have proven to be effective. As the computational technology progresses, more general approaches to a number of problems which have been treated previously by linearization and perturbation methods become feasible and rewarding.
Stochastic Partial Differential Equations And Related Fields
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Author : Andreas Eberle
language : en
Publisher: Springer
Release Date : 2018-07-03
Stochastic Partial Differential Equations And Related Fields written by Andreas Eberle and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-03 with Mathematics categories.
This Festschrift contains five research surveys and thirty-four shorter contributions by participants of the conference ''Stochastic Partial Differential Equations and Related Fields'' hosted by the Faculty of Mathematics at Bielefeld University, October 10–14, 2016. The conference, attended by more than 140 participants, including PostDocs and PhD students, was held both to honor Michael Röckner's contributions to the field on the occasion of his 60th birthday and to bring together leading scientists and young researchers to present the current state of the art and promising future developments. Each article introduces a well-described field related to Stochastic Partial Differential Equations and Stochastic Analysis in general. In particular, the longer surveys focus on Dirichlet forms and Potential theory, the analysis of Kolmogorov operators, Fokker–Planck equations in Hilbert spaces, the theory of variational solutions to stochastic partial differential equations, singular stochastic partial differential equations and their applications in mathematical physics, as well as on the theory of regularity structures and paracontrolled distributions. The numerous research surveys make the volume especially useful for graduate students and researchers who wish to start work in the above-mentioned areas, or who want to be informed about the current state of the art.
Stochastic Porous Media Equations
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Author : Viorel Barbu
language : en
Publisher: Springer
Release Date : 2016-09-30
Stochastic Porous Media Equations written by Viorel Barbu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-30 with Mathematics categories.
Focusing on stochastic porous media equations, this book places an emphasis on existence theorems, asymptotic behavior and ergodic properties of the associated transition semigroup. Stochastic perturbations of the porous media equation have reviously been considered by physicists, but rigorous mathematical existence results have only recently been found. The porous media equation models a number of different physical phenomena, including the flow of an ideal gas and the diffusion of a compressible fluid through porous media, and also thermal propagation in plasma and plasma radiation. Another important application is to a model of the standard self-organized criticality process, called the "sand-pile model" or the "Bak-Tang-Wiesenfeld model". The book will be of interest to PhD students and researchers in mathematics, physics and biology.
Stochastic Equations And Differential Geometry
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Author : Ya.I. Belopolskaya
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Stochastic Equations And Differential Geometry written by Ya.I. Belopolskaya 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.
'Et moi ..., si j'avait su comment en revenir, One service mathematics has rendered the je n'y serais point aile.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded n- sense'. The series is divergent; therefore we may be able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics ... '; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.