Stochastic Partial Differential Equations In Infinite Dimensional Spaces

Author : Michel Métivier
Publisher : Springer
Page : 160 pages
File Size : 51,5 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 : Leszek Gawarecki,Vidyadhar Mandrekar
Publisher : Springer Science & Business Media
Page : 300 pages
File Size : 49,9 Mb
Release : 2010-11-29
Category : Mathematics
ISBN : 9783642161940

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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 : Kiyosi Ito
Publisher : SIAM
Page : 79 pages
File Size : 51,5 Mb
Release : 1984-01-01
Category : Mathematics
ISBN : 1611970237

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Foundations of Stochastic Differential Equations in Infinite Dimensional Spaces by Kiyosi Ito Pdf

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.

Author : H Kunita,Hui-Hsiung Kuo
Publisher : CRC Press
Page : 340 pages
File Size : 43,8 Mb
Release : 1994-08-22
Category : Mathematics
ISBN : 0582244900

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Stochastic Analysis on Infinite Dimensional Spaces by H Kunita,Hui-Hsiung Kuo Pdf

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.)

Author : Wilfried Grecksch,Hannelore Lisei
Publisher : World Scientific
Page : 261 pages
File Size : 42,7 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 : 44,6 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 : Pao-Liu Chow
Publisher : CRC Press
Page : 336 pages
File Size : 45,7 Mb
Release : 2014-12-10
Category : Mathematics
ISBN : 9781466579552

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Stochastic Partial Differential Equations, Second Edition by Pao-Liu Chow Pdf

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.

Author : Da Prato Guiseppe,Zabczyk Jerzy,Professor Jerzy Zabczyk
Publisher : Unknown
Page : 128 pages
File Size : 52,6 Mb
Release : 2013-11-21
Category : Electronic
ISBN : 1306148065

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

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."

Author : Étienne Pardoux
Publisher : Springer Nature
Page : 74 pages
File Size : 51,8 Mb
Release : 2021-10-25
Category : Mathematics
ISBN : 9783030890032

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Stochastic Partial Differential Equations by Étienne Pardoux Pdf

This book gives a concise introduction to the classical theory of stochastic partial differential equations (SPDEs). It begins by describing the classes of equations which are studied later in the book, together with a list of motivating examples of SPDEs which are used in physics, population dynamics, neurophysiology, finance and signal processing. The central part of the book studies SPDEs as infinite-dimensional SDEs, based on the variational approach to PDEs. This extends both the classical Itô formulation and the martingale problem approach due to Stroock and Varadhan. The final chapter considers the solution of a space-time white noise-driven SPDE as a real-valued function of time and (one-dimensional) space. The results of J. Walsh's St Flour notes on the existence, uniqueness and Hölder regularity of the solution are presented. In addition, conditions are given under which the solution remains nonnegative, and the Malliavin calculus is applied. Lastly, reflected SPDEs and their connection with super Brownian motion are considered. At a time when new sophisticated branches of the subject are being developed, this book will be a welcome reference on classical SPDEs for newcomers to the theory.

Author : N.V. Krylov,M. Röckner,J. Zabczyk
Publisher : Springer
Page : 248 pages
File Size : 41,9 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 : Giuseppe Da Prato,Jerzy Zabczyk
Publisher : Cambridge University Press
Page : 513 pages
File Size : 40,5 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 : Sandra Cerrai
Publisher : Springer
Page : 332 pages
File Size : 40,7 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 : 45,6 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 : Hui-Hsiung Kuo,Ambar N. Sengupta,Padmanabhan Sundar
Publisher : World Scientific
Page : 257 pages
File Size : 41,7 Mb
Release : 2008
Category : Mathematics
ISBN : 9789812779557

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Infinite Dimensional Stochastic Analysis by Hui-Hsiung Kuo,Ambar N. Sengupta,Padmanabhan Sundar Pdf

This volume contains current work at the frontiers of research in infinite dimensional stochastic analysis. It presents a carefully chosen collection of articles by experts to highlight the latest developments in white noise theory, infinite dimensional transforms, quantum probability, stochastic partial differential equations, and applications to mathematical finance. Included in this volume are expository papers which will help increase communication between researchers working in these areas. The tools and techniques presented here will be of great value to research mathematicians, graduate students and applied mathematicians. Sample Chapter(s). Complex White Noise and the Infinite Dimensional Unitary Group (425 KB). Contents: Complex White Noise and the Infinite Dimensional Unitary Group (T Hida); Complex It Formulas (M Redfern); White Noise Analysis: Background and a Recent Application (J Becnel & A N Sengupta); Probability Measures with Sub-Additive Principal SzegAOCoJacobi Parameters (A Stan); Donsker''s Functional Calculus and Related Questions (P-L Chow & J Potthoff); Stochastic Analysis of Tidal Dynamics Equation (U Manna et al.); Adapted Solutions to the Backward Stochastic NavierOCoStokes Equations in 3D (P Sundar & H Yin); Spaces of Test and Generalized Functions of Arcsine White Noise Formulas (A Barhoumi et al.); An Infinite Dimensional Fourier-Mehler Transform and the L(r)vy Laplacian (K Saito & K Sakabe); The Heat Operator in Infinite Dimensions (B C Hall); Quantum Stochastic Dilation of Symmetric Covariant Completely Positive Semigroups with Unbounded Generator (D Goswami & K B Sinha); White Noise Analysis in the Theory of Three-Manifold Quantum Invariants (A Hahn); A New Explicit Formula for the Solution of the BlackOCoMertonOCoScholes Equation (J A Goldstein et al.); Volatility Models of the Yield Curve (V Goodman). Readership: Graduate-level researchers in stochastic analysis, mathematical physics and financial mathematic

Author : Kai Liu
Publisher : CRC Press
Page : 311 pages
File Size : 55,9 Mb
Release : 2005-08-23
Category : Mathematics
ISBN : 9781420034820

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Stability of Infinite Dimensional Stochastic Differential Equations with Applications by Kai Liu Pdf

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