Author : Xuerong Mao
Publisher : CRC Press
Page : 328 pages
File Size : 49,97 MB
Release : 1994-05-02
Category : Mathematics
ISBN : 9780824790806
This work presents a systematic study of current developments in stochastic differential delay equations driven by nonlinear integrators, detailing various exponential stabilities for stochastic differential equations and large-scale systems. It illustrates the practical use of stochastic stabilization, stochastic destabilization, stochastic flows, and stochastic oscillators in numerous real-world situations.
Author : Rafail Khasminskii
Publisher : Springer Science & Business Media
Page : 353 pages
File Size : 10,60 MB
Release : 2011-09-20
Category : Mathematics
ISBN : 3642232809
Since the publication of the first edition of the present volume in 1980, the stochastic stability of differential equations has become a very popular subject of research in mathematics and engineering. To date exact formulas for the Lyapunov exponent, the criteria for the moment and almost sure stability, and for the existence of stationary and periodic solutions of stochastic differential equations have been widely used in the literature. In this updated volume readers will find important new results on the moment Lyapunov exponent, stability index and some other fields, obtained after publication of the first edition, and a significantly expanded bibliography. This volume provides a solid foundation for students in graduate courses in mathematics and its applications. It is also useful for those researchers who would like to learn more about this subject, to start their research in this area or to study the properties of concrete mechanical systems subjected to random perturbations.
Author : Xuerong Mao
Publisher : Imperial College Press
Page : 430 pages
File Size : 31,99 MB
Release : 2006
Category : Mathematics
ISBN : 1860947018
This textbook provides the first systematic presentation of the theory of stochastic differential equations with Markovian switching. It presents the basic principles at an introductory level but emphasizes current advanced level research trends. The material takes into account all the features of Ito equations, Markovian switching, interval systems and time-lag. The theory developed is applicable in different and complicated situations in many branches of science and industry.
Author : Leonid Shaikhet
Publisher : Springer Science & Business Media
Page : 352 pages
File Size : 26,81 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 : Kai Liu
Publisher : CRC Press
Page : 311 pages
File Size : 27,49 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 : Jianhai Bao
Publisher : Springer
Page : 159 pages
File Size : 38,48 MB
Release : 2016-11-19
Category : Mathematics
ISBN : 3319469797
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.
Author : Takeshi Taniguchi
Publisher :
Page : 11 pages
File Size : 28,49 MB
Release : 1997
Category :
ISBN :
Author : Kai Liu
Publisher : Cambridge University Press
Page : 277 pages
File Size : 32,61 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 : Hui-Hsiung Kuo
Publisher : Springer Science & Business Media
Page : 290 pages
File Size : 47,32 MB
Release : 2006-02-04
Category : Mathematics
ISBN : 0387310576
Also called Ito calculus, the theory of stochastic integration has applications in virtually every scientific area involving random functions. This introductory textbook provides a concise introduction to the Ito calculus. From the reviews: "Introduction to Stochastic Integration is exactly what the title says. I would maybe just add a ‘friendly’ introduction because of the clear presentation and flow of the contents." --THE MATHEMATICAL SCIENCES DIGITAL LIBRARY
Author : S. E. A. Mohammed
Publisher : Pitman Advanced Publishing Program
Page : 268 pages
File Size : 34,14 MB
Release : 1984
Category : Mathematics
ISBN :
