Author : S. Peszat
Publisher : Cambridge University Press
Page : 45 pages
File Size : 15,70 MB
Release : 2007-10-11
Category : Mathematics
ISBN : 0521879892
Comprehensive monograph by two leading international experts; includes applications to statistical and fluid mechanics and to finance.
Author : Peter H. Baxendale
Publisher : World Scientific
Page : 416 pages
File Size : 15,96 MB
Release : 2007
Category : Science
ISBN : 9812706623
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.
Author : Wilfried Grecksch
Publisher : De Gruyter Akademie Forschung
Page : 188 pages
File Size : 11,25 MB
Release : 1995
Category : Mathematics
ISBN :
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.
Author : Kai Liu
Publisher : Cambridge University Press
Page : 277 pages
File Size : 18,79 MB
Release : 2019-05-02
Category : Mathematics
ISBN : 1108626491
The stability of stochastic differential equations in abstract, mainly Hilbert, spaces receives a unified treatment in this self-contained book. It covers basic theory as well as computational techniques for handling the stochastic stability of systems from mathematical, physical and biological problems. Its core material is divided into three parts devoted respectively to the stochastic stability of linear systems, non-linear systems, and time-delay systems. The focus is on stability of stochastic dynamical processes affected by white noise, which are described by partial differential equations such as the Navier–Stokes equations. A range of mathematicians and scientists, including those involved in numerical computation, will find this book useful. It is also ideal for engineers working on stochastic systems and their control, and researchers in mathematical physics or biology.
Author : Kazufumi Ito
Publisher : World Scientific
Page : 524 pages
File Size : 30,68 MB
Release : 2002
Category : Science
ISBN : 9789812380265
Annotation Ito (North Carolina State U.) and Kappel (U. of Graz, Austria) offer a unified presentation of the general approach for well-posedness results using abstract evolution equations, drawing from and modifying the work of K. and Y. Kobayashi and S. Oharu. They also explore abstract approximation results for evolution equations. Their work is not a textbook, but they explain how instructors can use various sections, or combinations of them, as a foundation for a range of courses. Annotation copyrighted by Book News, Inc., Portland, OR
Author : Salah-Eldin Mohammed
Publisher : American Mathematical Soc.
Page : 120 pages
File Size : 23,57 MB
Release : 2008
Category : Mathematics
ISBN : 0821842501
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 : Kai Liu
Publisher : CRC Press
Page : 311 pages
File Size : 45,59 MB
Release : 2005-08-23
Category : Mathematics
ISBN : 1420034820
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
Author : Simo Särkkä
Publisher : Cambridge University Press
Page : 327 pages
File Size : 13,36 MB
Release : 2019-05-02
Category : Business & Economics
ISBN : 1316510085
With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.
Author : Leonid Shaikhet
Publisher : Springer Science & Business Media
Page : 352 pages
File Size : 26,27 MB
Release : 2013-03-29
Category : Technology & Engineering
ISBN : 3319001019
Stability conditions for functional differential equations can be obtained using Lyapunov functionals. Lyapunov Functionals and Stability of Stochastic Functional Differential Equations describes the general method of construction of Lyapunov functionals to investigate the stability of differential equations with delays. This work continues and complements the author’s previous book Lyapunov Functionals and Stability of Stochastic Difference Equations, where this method is described for difference equations with discrete and continuous time. The text begins with both a description and a delineation of the peculiarities of deterministic and stochastic functional differential equations. There follows basic definitions for stability theory of stochastic hereditary systems, and the formal procedure of Lyapunov functionals construction is presented. Stability investigation is conducted for stochastic linear and nonlinear differential equations with constant and distributed delays. The proposed method is used for stability investigation of different mathematical models such as: • inverted controlled pendulum; • Nicholson's blowflies equation; • predator-prey relationships; • epidemic development; and • mathematical models that describe human behaviours related to addictions and obesity. Lyapunov Functionals and Stability of Stochastic Functional Differential Equations is primarily addressed to experts in stability theory but will also be of interest to professionals and students in pure and computational mathematics, physics, engineering, medicine, and biology.
Author : Ioėlʹ Gilʹevich Malkin
Publisher :
Page : 474 pages
File Size : 12,34 MB
Release : 1959
Category : Motion
ISBN :
