Stochastic Evolution Equations
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Stochastic Evolution Equations
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Author : Wilfried Grecksch
language : en
Publisher: De Gruyter Akademie Forschung
Release Date : 1995
Stochastic Evolution Equations written by Wilfried Grecksch and has been published by De Gruyter Akademie Forschung this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.
The authors give a self-contained exposition of the theory of stochastic evolution equations. Elements of infinite dimensional analysis, martingale theory in Hilbert spaces, stochastic integrals, stochastic convolutions are applied. Existence and uniqueness theorems for stochastic evolution equations in Hilbert spaces in the sense of the semigroup theory, the theory of evolution operators, and monotonous operators in rigged Hilbert spaces are discussed. Relationships between the different concepts are demonstrated. The results are used to concrete stochastic partial differential equations like parabolic and hyperbolic Ito equations and random constitutive equations of elastic viscoplastic materials. Furthermore, stochastic evolution equations in rigged Hilbert spaces are approximated by time discretization methods.
Discovering Evolution Equations With Applications
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Author : Mark McKibben
language : en
Publisher: CRC Press
Release Date : 2011-06-03
Discovering Evolution Equations With Applications written by Mark McKibben and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-03 with Mathematics categories.
Most existing books on evolution equations tend either to cover a particular class of equations in too much depth for beginners or focus on a very specific research direction. Thus, the field can be daunting for newcomers to the field who need access to preliminary material and behind-the-scenes detail. Taking an applications-oriented, conversation
Strong And Weak Approximation Of Semilinear Stochastic Evolution Equations
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Author : Raphael Kruse
language : en
Publisher: Springer
Release Date : 2013-11-18
Strong And Weak Approximation Of Semilinear Stochastic Evolution Equations written by Raphael Kruse and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-18 with Mathematics categories.
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.
General Pontryagin Type Stochastic Maximum Principle And Backward Stochastic Evolution Equations In Infinite Dimensions
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Author : Qi Lü
language : en
Publisher: Springer
Release Date : 2014-06-02
General Pontryagin Type Stochastic Maximum Principle And Backward Stochastic Evolution Equations In Infinite Dimensions written by Qi Lü and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-02 with Science categories.
The classical Pontryagin maximum principle (addressed to deterministic finite dimensional control systems) is one of the three milestones in modern control theory. The corresponding theory is by now well-developed in the deterministic infinite dimensional setting and for the stochastic differential equations. However, very little is known about the same problem but for controlled stochastic (infinite dimensional) evolution equations when the diffusion term contains the control variables and the control domains are allowed to be non-convex. Indeed, it is one of the longstanding unsolved problems in stochastic control theory to establish the Pontryagin type maximum principle for this kind of general control systems: this book aims to give a solution to this problem. This book will be useful for both beginners and experts who are interested in optimal control theory for stochastic evolution equations.
General Pontryagin Type Stochastic Maximum Principle And Backward Stochastic Evolution Equations In Infinite Dimensions
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Author : Qi Lu
language : en
Publisher:
Release Date : 2014-06-30
General Pontryagin Type Stochastic Maximum Principle And Backward Stochastic Evolution Equations In Infinite Dimensions written by Qi Lu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-30 with categories.
Stochastic Differential Equations
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Author : Peter H. Baxendale
language : en
Publisher: World Scientific
Release Date : 2007
Stochastic Differential Equations written by Peter H. Baxendale and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Science categories.
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 attention of mathematicians of all generations, because, together with a short but thorough introduction to SPDEs, it presents a number of optimal and essentially non-improvable results about solvability for a large class of both linear and non-linear equations.
Stochastic Evolution Systems
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Author : Boris L. Rozovsky
language : en
Publisher: Springer
Release Date : 2018-10-03
Stochastic Evolution Systems written by Boris L. Rozovsky and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-03 with Mathematics categories.
This monograph, now in a thoroughly revised second edition, develops the theory of stochastic calculus in Hilbert spaces and applies the results to the study of generalized solutions of stochastic parabolic equations. The emphasis lies on second-order stochastic parabolic equations and their connection to random dynamical systems. The authors further explore applications to the theory of optimal non-linear filtering, prediction, and smoothing of partially observed diffusion processes. The new edition now also includes a chapter on chaos expansion for linear stochastic evolution systems. This book will appeal to anyone working in disciplines that require tools from stochastic analysis and PDEs, including pure mathematics, financial mathematics, engineering and physics.
Stochastic Evolution Equations And White Noise Analysis
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Author : Yoshio Miyahara
language : en
Publisher: Department of Mathematics and Statistics, Carleton University
Release Date : 1982
Stochastic Evolution Equations And White Noise Analysis written by Yoshio Miyahara and has been published by Department of Mathematics and Statistics, Carleton University this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with Gaussian processes categories.
Stochastic Differential Equations Theory And Applications
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Author :
language : en
Publisher:
Release Date :
Stochastic Differential Equations Theory And Applications written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with 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.