The Stable Manifold Theorem for Semilinear Stochastic Evolution Equations and Stochastic Partial Differential Equations PDF Download
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Author: Salah-Eldin Mohammed
Publisher: American Mathematical Soc.
ISBN: 0821842501
Category : Mathematics
Languages : en
Pages : 120
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Book Description
The main objective of this paper is to characterize the pathwise local structure of solutions of semilinear stochastic evolution equations and stochastic partial differential equations near stationary solutions.
Author: Salah-Eldin Mohammed
Publisher: American Mathematical Soc.
ISBN: 0821842501
Category : Mathematics
Languages : en
Pages : 120
Get Book Here
Book Description
The main objective of this paper is to characterize the pathwise local structure of solutions of semilinear stochastic evolution equations and stochastic partial differential equations near stationary solutions.
Author:
Publisher:
ISBN: 9781470405236
Category : Evolution equations
Languages : en
Pages : 105
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Book Description
Author: Pao-Liu Chow
Publisher: CRC Press
ISBN: 1466579579
Category : Mathematics
Languages : en
Pages : 334
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Book Description
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 Levy type of noise. Stochastic Partial Differential Equations, Second Edition incorporates these recent developments and impro
Author: Peter H. Baxendale
Publisher: World Scientific
ISBN: 9812770631
Category : Mathematics
Languages : en
Pages : 416
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Book Description
This volume consists of 15 articles written by experts in stochastic analysis. The first paper in the volume, Stochastic Evolution Equations by N V Krylov and B L Rozovskii, was originally published in Russian in 1979. After more than a quarter-century, this paper remains a standard reference in the field of stochastic partial differential equations (SPDEs) and continues to attract the attention of mathematicians of all generations. Together with a short but thorough introduction to SPDEs, it presents a number of optimal, and essentially unimprovable, results about solvability for a large class of both linear and non-linear equations. The other papers in this volume were specially written for the occasion of Prof RozovskiiOCOs 60th birthday. They tackle a wide range of topics in the theory and applications of stochastic differential equations, both ordinary and with partial derivatives."
Author: Giuseppe Da Prato
Publisher:
ISBN: 9783662210840
Category :
Languages : en
Pages : 0
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Book Description
Author: Mickaël D. Chekroun
Publisher: Springer
ISBN: 3319125206
Category : Mathematics
Languages : en
Pages : 141
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Book Description
In this second volume, a general approach is developed to provide approximate parameterizations of the "small" scales by the "large" ones for a broad class of stochastic partial differential equations (SPDEs). This is accomplished via the concept of parameterizing manifolds (PMs), which are stochastic manifolds that improve, for a given realization of the noise, in mean square error the partial knowledge of the full SPDE solution when compared to its projection onto some resolved modes. Backward-forward systems are designed to give access to such PMs in practice. The key idea consists of representing the modes with high wave numbers as a pullback limit depending on the time-history of the modes with low wave numbers. Non-Markovian stochastic reduced systems are then derived based on such a PM approach. The reduced systems take the form of stochastic differential equations involving random coefficients that convey memory effects. The theory is illustrated on a stochastic Burgers-type equation.
Author: Raphael Kruse
Publisher: Springer
ISBN: 3319022318
Category : Mathematics
Languages : en
Pages : 188
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Book Description
In this book we analyze the error caused by numerical schemes for the approximation of semilinear stochastic evolution equations (SEEq) in a Hilbert space-valued setting. The numerical schemes considered combine Galerkin finite element methods with Euler-type temporal approximations. Starting from a precise analysis of the spatio-temporal regularity of the mild solution to the SEEq, we derive and prove optimal error estimates of the strong error of convergence in the first part of the book. The second part deals with a new approach to the so-called weak error of convergence, which measures the distance between the law of the numerical solution and the law of the exact solution. This approach is based on Bismut’s integration by parts formula and the Malliavin calculus for infinite dimensional stochastic processes. These techniques are developed and explained in a separate chapter, before the weak convergence is proven for linear SEEq.
Author: Étienne Pardoux
Publisher: Springer Nature
ISBN: 3030890031
Category : Mathematics
Languages : en
Pages : 74
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Book Description
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: Giuseppe Da Prato
Publisher: CRC Press
ISBN: 1420028723
Category : Mathematics
Languages : en
Pages : 360
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Book Description
Stochastic Partial Differential Equations and Applications gives an overview of current state-of-the-art stochastic PDEs in several fields, such as filtering theory, stochastic quantization, quantum probability, and mathematical finance. Featuring contributions from leading expert participants at an international conference on the subject, this boo
Author: Peter Kotelenez
Publisher: Springer Science & Business Media
ISBN: 0387743170
Category : Mathematics
Languages : en
Pages : 452
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Book Description
Stochastic Partial Differential Equations analyzes mathematical models of time-dependent physical phenomena on microscopic, macroscopic and mesoscopic levels. It provides a rigorous derivation of each level from the preceding one and examines the resulting mesoscopic equations in detail. Coverage first describes the transition from the microscopic equations to the mesoscopic equations. It then covers a general system for the positions of the large particles.
