Evolution Equations
Evolution Equations

Author: Kaïs Ammari

Publisher: Cambridge University Press

Published: 2018

Total Pages: 205

ISBN-13: 1108412300

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The proceedings of a summer school held in 2015 whose theme was long time behavior and control of evolution equations.

Markov Processes, Feller Semigroups and Evolution Equations
Markov Processes, Feller Semigroups and Evolution Equations

Author: J. A. van Casteren

Publisher: World Scientific

Published: 2011

Total Pages: 825

ISBN-13: 9814322180

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The book provides a systemic treatment of time-dependent strong Markov processes with values in a Polish space. It describes its generators and the link with stochastic differential equations in infinite dimensions. In a unifying way, where the square gradient operator is employed, new results for backward stochastic differential equations and long-time behavior are discussed in depth. The book also establishes a link between propagators or evolution families with the Feller property and time-inhomogeneous Markov processes. This mathematical material finds its applications in several branches of the scientific world, among which are mathematical physics, hedging models in financial mathematics, and population models.

Stochastic Evolution Equations
Stochastic Evolution Equations

Author: Wilfried Grecksch

Publisher: De Gruyter Akademie Forschung

Published: 1995

Total Pages: 188

ISBN-13:

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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.

Stochastic Partial Differential Equations
Stochastic Partial Differential Equations

Author: Pao-Liu Chow

Publisher: CRC Press

Published: 2007-03-19

Total Pages: 294

ISBN-13: 1420010301

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As a relatively new area in mathematics, stochastic partial differential equations (PDEs) are still at a tender age and have not yet received much attention in the mathematical community. Filling the void of an introductory text in the field, Stochastic Partial Differential Equations introduces PDEs to students familiar with basic probability theor

Asymptotic Analysis for Functional Stochastic Differential Equations
Asymptotic Analysis for Functional Stochastic Differential Equations

Author: Jianhai Bao

Publisher: Springer

Published: 2016-11-19

Total Pages: 159

ISBN-13: 3319469797

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This brief treats dynamical systems that involve delays and random disturbances. The study is motivated by a wide variety of systems in real life in which random noise has to be taken into consideration and the effect of delays cannot be ignored. Concentrating on such systems that are described by functional stochastic differential equations, this work focuses on the study of large time behavior, in particular, ergodicity.This brief is written for probabilists, applied mathematicians, engineers, and scientists who need to use delay systems and functional stochastic differential equations in their work. Selected topics from the brief can also be used in a graduate level topics course in probability and stochastic processes.

Evolution Equations
Evolution Equations

Author: Gisele Ruiz Goldstein

Publisher: CRC Press

Published: 2003-06-24

Total Pages: 442

ISBN-13: 9780824709754

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Celebrating the work of renowned mathematician Jerome A. Goldstein, this reference compiles original research on the theory and application of evolution equations to stochastics, physics, engineering, biology, and finance. The text explores a wide range of topics in linear and nonlinear semigroup theory, operator theory, functional analysis, and linear and nonlinear partial differential equations, and studies the latest theoretical developments and uses of evolution equations in a variety of disciplines. Providing nearly 500 references, the book contains discussions by renowned mathematicians such as H. Brezis, G. Da Prato, N.E. Gretskij, I. Lasiecka, Peter Lax, M. M. Rao, and R. Triggiani.

Stochastic Partial Differential Equations, Second Edition
Stochastic Partial Differential Equations, Second Edition

Author: Pao-Liu Chow

Publisher: CRC Press

Published: 2014-12-10

Total Pages: 336

ISBN-13: 1466579552

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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.