Stochastic Differential Equations In Infinite Dimensional Spaces And Their Applications
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Stochastic Equations In Infinite Dimensions
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Author : Guiseppe Da Prato
language : en
Publisher: Cambridge University Press
Release Date : 1992-12-03
Stochastic Equations In Infinite Dimensions written by Guiseppe Da Prato and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-12-03 with Mathematics categories.
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.
Stochastic Differential Equations In Infinite Dimensional Spaces And Their Applications
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Author : J. R. Dorrah
language : en
Publisher:
Release Date : 1984
Stochastic Differential Equations In Infinite Dimensional Spaces And Their Applications written by J. R. Dorrah and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with categories.
Stochastic Optimal Control In Infinite Dimension
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Author : Giorgio Fabbri
language : en
Publisher: Springer
Release Date : 2017-06-22
Stochastic Optimal Control In Infinite Dimension written by Giorgio Fabbri and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-22 with Mathematics categories.
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.
Stochastic Equations In Infinite Dimensions
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Author : Giuseppe Da Prato
language : en
Publisher: Cambridge University Press
Release Date : 2014-04-17
Stochastic Equations In Infinite Dimensions written by Giuseppe Da Prato and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-04-17 with Mathematics categories.
Updates in this second edition include two brand new chapters and an even more comprehensive bibliography.
Stochastic Differential Equations In Infinite Dimensional Spaces
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Author : G. Kallianpur
language : en
Publisher: IMS
Release Date : 1995
Stochastic Differential Equations In Infinite Dimensional Spaces written by G. Kallianpur and has been published by IMS this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.
An Introduction To Infinite Dimensional Analysis
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Author : Giuseppe Da Prato
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-08-25
An Introduction To Infinite Dimensional Analysis written by Giuseppe Da Prato 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 2006-08-25 with Mathematics categories.
Based on well-known lectures given at Scuola Normale Superiore in Pisa, this book introduces analysis in a separable Hilbert space of infinite dimension. It starts from the definition of Gaussian measures in Hilbert spaces, concepts such as the Cameron-Martin formula, Brownian motion and Wiener integral are introduced in a simple way. These concepts are then used to illustrate basic stochastic dynamical systems and Markov semi-groups, paying attention to their long-time behavior.
Introduction To Infinite Dimensional Stochastic Analysis
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Author : Zhi-yuan Huang
language : en
Publisher: Springer Science & Business Media
Release Date : 2000
Introduction To Infinite Dimensional Stochastic Analysis written by Zhi-yuan Huang 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 2000 with Mathematics categories.
This book offers a concise introduction to the rapidly expanding field of infinite dimensional stochastic analysis. It treats Malliavin calculus and white noise analysis in a single book, presenting these two different areas in a unified setting of Gaussian probability spaces. Topics include recent results and developments in the areas of quasi-sure analysis, anticipating stochastic calculus, generalised operator theory and applications in quantum physics. A short overview on the foundations of infinite dimensional analysis is given. Audience: This volume will be of interest to researchers and graduate students whose work involves probability theory, stochastic processes, functional analysis, operator theory, mathematics of physics and abstract harmonic analysis.
Topological Vector Spaces And Their Applications
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Author : V.I. Bogachev
language : en
Publisher: Springer
Release Date : 2017-05-16
Topological Vector Spaces And Their Applications written by V.I. Bogachev and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-16 with Mathematics categories.
This book gives a compact exposition of the fundamentals of the theory of locally convex topological vector spaces. Furthermore it contains a survey of the most important results of a more subtle nature, which cannot be regarded as basic, but knowledge which is useful for understanding applications. Finally, the book explores some of such applications connected with differential calculus and measure theory in infinite-dimensional spaces. These applications are a central aspect of the book, which is why it is different from the wide range of existing texts on topological vector spaces. Overall, this book develops differential and integral calculus on infinite-dimensional locally convex spaces by using methods and techniques of the theory of locally convex spaces. The target readership includes mathematicians and physicists whose research is related to infinite-dimensional analysis.
Stochastic Analysis On Infinite Dimensional Spaces
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Author : H Kunita
language : en
Publisher: CRC Press
Release Date : 1994-08-22
Stochastic Analysis On Infinite Dimensional Spaces written by H Kunita and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-08-22 with Mathematics categories.
The book discusses the following topics in stochastic analysis: 1. Stochastic analysis related to Lie groups: stochastic analysis of loop spaces and infinite dimensional manifolds has been developed rapidly after the fundamental works of Gross and Malliavin. (Lectures by Driver, Gross, Mitoma, and Sengupta.)
Stability Of Infinite Dimensional Stochastic Differential Equations With Applications
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Author : Kai Liu
language : en
Publisher: CRC Press
Release Date : 2005-08-23
Stability Of Infinite Dimensional Stochastic Differential Equations With Applications written by Kai Liu and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-08-23 with Mathematics categories.
Stochastic differential equations in infinite dimensional spaces are motivated by the theory and analysis of stochastic processes and by applications such as stochastic control, population biology, and turbulence, where the analysis and control of such systems involves investigating their stability. While the theory of such equations is well establ