Stochastic Pde S And Kolmogorov Equations In Infinite Dimensions

Author : N.V. Krylov,M. Röckner,J. Zabczyk
Publisher : Springer
Page : 248 pages
File Size : 42,7 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540481614

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Stochastic PDE's and Kolmogorov Equations in Infinite Dimensions by N.V. Krylov,M. Röckner,J. Zabczyk Pdf

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.

Author : Sandra Cerrai
Publisher : Springer
Page : 332 pages
File Size : 46,9 Mb
Release : 2003-07-01
Category : Mathematics
ISBN : 9783540451471

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Second Order PDE's in Finite and Infinite Dimension by Sandra Cerrai Pdf

The main objective of this monograph is the study of a class of stochastic differential systems having unbounded coefficients, both in finite and in infinite dimension. We focus our attention on the regularity properties of the solutions and hence on the smoothing effect of the corresponding transition semigroups in the space of bounded and uniformly continuous functions. As an application of these results, we study the associated Kolmogorov equations, the large-time behaviour of the solutions and some stochastic optimal control problems together with the corresponding Hamilton- Jacobi-Bellman equations. In the literature there exists a large number of works (mostly in finite dimen sion) dealing with these arguments in the case of bounded Lipschitz-continuous coefficients and some of them concern the case of coefficients having linear growth. Few papers concern the case of non-Lipschitz coefficients, but they are mainly re lated to the study of the existence and the uniqueness of solutions for the stochastic system. Actually, the study of any further properties of those systems, such as their regularizing properties or their ergodicity, seems not to be developed widely enough. With these notes we try to cover this gap.

Author : Giuseppe Da Prato,Jerzy Zabczyk
Publisher : Cambridge University Press
Page : 513 pages
File Size : 43,6 Mb
Release : 2014-04-17
Category : Mathematics
ISBN : 9781139917155

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Stochastic Equations in Infinite Dimensions by Giuseppe Da Prato,Jerzy Zabczyk Pdf

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.

Author : Giuseppe Da Prato,Jerzy Zabczyk
Publisher : Cambridge University Press
Page : 513 pages
File Size : 40,7 Mb
Release : 2014-04-17
Category : Mathematics
ISBN : 9781107055841

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Stochastic Equations in Infinite Dimensions by Giuseppe Da Prato,Jerzy Zabczyk Pdf

Updates in this second edition include two brand new chapters and an even more comprehensive bibliography.

Author : Leszek Gawarecki,Vidyadhar Mandrekar
Publisher : Springer
Page : 291 pages
File Size : 41,5 Mb
Release : 2013-01-27
Category : Mathematics
ISBN : 3642266347

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Stochastic Differential Equations in Infinite Dimensions by Leszek Gawarecki,Vidyadhar Mandrekar Pdf

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.

Author : Giuseppe Da Prato
Publisher : Birkhäuser
Page : 182 pages
File Size : 51,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034879095

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Kolmogorov Equations for Stochastic PDEs by Giuseppe Da Prato Pdf

Kolmogorov Equations for Stochastic PDEs gives an introduction to stochastic partial differential equations, such as reaction-diffusion, Burgers and 2D Navier-Stokes equations, perturbed by noise. It studies several properties of corresponding transition semigroups, such as Feller and strong Feller properties, irreducibility, existence and uniqueness of invariant measures. In addition, the transition semigroups are interpreted as generalized solutions of Kologorov equations.

Author : Anonim
Publisher : Unknown
Page : 239 pages
File Size : 50,9 Mb
Release : 1999
Category : Electronic
ISBN : OCLC:860264714

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Stochastic PDE's and Kolmogorov Equations in Infinite Dimensions by Anonim Pdf

Author : Michel Métivier
Publisher : Springer
Page : 160 pages
File Size : 49,7 Mb
Release : 1988-10
Category : Mathematics
ISBN : UOM:39015018451008

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Stochastic Partial Differential Equations in Infinite Dimensional Spaces by Michel Métivier Pdf

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.

Author : Wilfried Grecksch,Hannelore Lisei
Publisher : World Scientific
Page : 261 pages
File Size : 46,5 Mb
Release : 2020-04-22
Category : Science
ISBN : 9789811209802

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Infinite Dimensional And Finite Dimensional Stochastic Equations And Applications In Physics by Wilfried Grecksch,Hannelore Lisei Pdf

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.

Author : G. Kallianpur,Jie Xiong
Publisher : IMS
Page : 356 pages
File Size : 48,7 Mb
Release : 1995
Category : Mathematics
ISBN : 0940600382

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Stochastic Differential Equations in Infinite Dimensional Spaces by G. Kallianpur,Jie Xiong Pdf

Author : Nikolaĭ Vladimirovich Krylov
Publisher : Unknown
Page : 239 pages
File Size : 46,5 Mb
Release : 1999
Category : Diffusion processes
ISBN : LCCN:99051992

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Stochastic PDE's and Kolmogorov Equations in Infinite Dimensions by Nikolaĭ Vladimirovich Krylov Pdf

Author : Guiseppe Da Prato,Jerzy Zabczyk
Publisher : Cambridge University Press
Page : 474 pages
File Size : 40,6 Mb
Release : 1992-12-03
Category : Mathematics
ISBN : 9780521385299

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Stochastic Equations in Infinite Dimensions by Guiseppe Da Prato,Jerzy Zabczyk Pdf

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.

Author : Giuseppe Da Prato
Publisher : Springer Science & Business Media
Page : 217 pages
File Size : 55,6 Mb
Release : 2006-08-25
Category : Mathematics
ISBN : 9783540290216

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An Introduction to Infinite-Dimensional Analysis by Giuseppe Da Prato Pdf

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.

Author : Davar Khoshnevisan
Publisher : American Mathematical Soc.
Page : 127 pages
File Size : 53,6 Mb
Release : 2014-06-11
Category : Mathematics
ISBN : 9781470415471

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Analysis of Stochastic Partial Differential Equations by Davar Khoshnevisan Pdf

The general area of stochastic PDEs is interesting to mathematicians because it contains an enormous number of challenging open problems. There is also a great deal of interest in this topic because it has deep applications in disciplines that range from applied mathematics, statistical mechanics, and theoretical physics, to theoretical neuroscience, theory of complex chemical reactions [including polymer science], fluid dynamics, and mathematical finance. The stochastic PDEs that are studied in this book are similar to the familiar PDE for heat in a thin rod, but with the additional restriction that the external forcing density is a two-parameter stochastic process, or what is more commonly the case, the forcing is a "random noise," also known as a "generalized random field." At several points in the lectures, there are examples that highlight the phenomenon that stochastic PDEs are not a subset of PDEs. In fact, the introduction of noise in some partial differential equations can bring about not a small perturbation, but truly fundamental changes to the system that the underlying PDE is attempting to describe. The topics covered include a brief introduction to the stochastic heat equation, structure theory for the linear stochastic heat equation, and an in-depth look at intermittency properties of the solution to semilinear stochastic heat equations. Specific topics include stochastic integrals à la Norbert Wiener, an infinite-dimensional Itô-type stochastic integral, an example of a parabolic Anderson model, and intermittency fronts. There are many possible approaches to stochastic PDEs. The selection of topics and techniques presented here are informed by the guiding example of the stochastic heat equation. A co-publication of the AMS and CBMS.

Author : Giorgio Fabbri,Fausto Gozzi,Andrzej Święch
Publisher : Springer
Page : 916 pages
File Size : 40,5 Mb
Release : 2017-06-22
Category : Mathematics
ISBN : 9783319530673

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Stochastic Optimal Control in Infinite Dimension by Giorgio Fabbri,Fausto Gozzi,Andrzej Święch Pdf

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.