Stochastic Partial Differential Equations In Infinite Dimensional Spaces
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Stochastic Partial Differential Equations In Infinite Dimensional Spaces
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Author : Michel Métivier
language : en
Publisher: Springer
Release Date : 1988-10
Stochastic Partial Differential Equations In Infinite Dimensional Spaces written by Michel Métivier and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-10 with Mathematics categories.
While this book was being printed, the news of Michel Métivier's premature death arrived at the Scuola Normale Superiore. The present book originated from a series of lectures Michel Métivier held at the Scuola Normale during the years 1986 and 1987. The subject of these lectures was the analysis of weak solutions to stochastic partial equations, a topic that requires a deep knowledge of nonlinear functional analysis and probability. A vast literature, involving a number of applications to various scientific fields is devoted to this problem and many different approaches have been developed. In his lectures Métivier gave a new treatment of the subject, which unifies the theory and provides several new results. The power of his new approach has not yet been fully exploited and would certainly have led him to further interesting developments. For this reason, besides the invaluable enthusiasm in life he was able to communicate to everybody, his recent premature departure is even more painful.
Stochastic Differential Equations In Infinite Dimensions
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Author : Leszek Gawarecki
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-11-29
Stochastic Differential Equations In Infinite Dimensions written by Leszek Gawarecki 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 2010-11-29 with Mathematics categories.
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.
Foundations Of Stochastic Differential Equations In Infinite Dimensional Spaces
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Author : Kiyosi Ito
language : en
Publisher: SIAM
Release Date : 1984-01-01
Foundations Of Stochastic Differential Equations In Infinite Dimensional Spaces written by Kiyosi Ito and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984-01-01 with Mathematics categories.
A systematic, self-contained treatment of the theory of stochastic differential equations in infinite dimensional spaces. Included is a discussion of Schwartz spaces of distributions in relation to probability theory and infinite dimensional stochastic analysis, as well as the random variables and stochastic processes that take values in infinite dimensional spaces.
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.)
Infinite Dimensional And Finite Dimensional Stochastic Equations And Applications In Physics
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Author : Wilfried Grecksch
language : en
Publisher: World Scientific
Release Date : 2020-04-22
Infinite Dimensional And Finite Dimensional Stochastic Equations And Applications In Physics written by Wilfried Grecksch and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-22 with Science categories.
This volume contains survey articles on various aspects of stochastic partial differential equations (SPDEs) and their applications in stochastic control theory and in physics.The topics presented in this volume are:This book is intended not only for graduate students in mathematics or physics, but also for mathematicians, mathematical physicists, theoretical physicists, and science researchers interested in the physical applications of the theory of stochastic processes.
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.
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.
Stochastic Pde S And Kolmogorov Equations In Infinite Dimensions
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Author : N.V. Krylov
language : en
Publisher: Springer
Release Date : 2006-11-15
Stochastic Pde S And Kolmogorov Equations In Infinite Dimensions written by N.V. Krylov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
Kolmogorov equations are second order parabolic equations with a finite or an infinite number of variables. They are deeply connected with stochastic differential equations in finite or infinite dimensional spaces. They arise in many fields as Mathematical Physics, Chemistry and Mathematical Finance. These equations can be studied both by probabilistic and by analytic methods, using such tools as Gaussian measures, Dirichlet Forms, and stochastic calculus. The following courses have been delivered: N.V. Krylov presented Kolmogorov equations coming from finite-dimensional equations, giving existence, uniqueness and regularity results. M. Röckner has presented an approach to Kolmogorov equations in infinite dimensions, based on an LP-analysis of the corresponding diffusion operators with respect to suitably chosen measures. J. Zabczyk started from classical results of L. Gross, on the heat equation in infinite dimension, and discussed some recent results.
Stochastic Partial Differential Equations Second Edition
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Author : Pao-Liu Chow
language : en
Publisher: CRC Press
Release Date : 2014-12-10
Stochastic Partial Differential Equations Second Edition written by Pao-Liu Chow and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-10 with Mathematics categories.
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 Lévy type of noise. Stochastic Partial Differential Equations, Second Edition incorporates these recent developments and improves the presentation of material. New to the Second Edition Two sections on the Lévy type of stochastic integrals and the related stochastic differential equations in finite dimensions Discussions of Poisson random fields and related stochastic integrals, the solution of a stochastic heat equation with Poisson noise, and mild solutions to linear and nonlinear parabolic equations with Poisson noises Two sections on linear and semilinear wave equations driven by the Poisson type of noises Treatment of the Poisson stochastic integral in a Hilbert space and mild solutions of stochastic evolutions with Poisson noises Revised proofs and new theorems, such as explosive solutions of stochastic reaction diffusion equations Additional applications of stochastic PDEs to population biology and finance Updated section on parabolic equations and related elliptic problems in Gauss–Sobolev spaces The book covers basic theory as well as computational and analytical techniques to solve physical, biological, and financial problems. It first presents classical concrete problems before proceeding to a unified theory of stochastic evolution equations and describing applications, such as turbulence in fluid dynamics, a spatial population growth model in a random environment, and a stochastic model in bond market theory. The author also explores the connection of stochastic PDEs to infinite-dimensional stochastic analysis.
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.
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.