Stochastic Stability Of Differential Equations

Author : Rafail Khasminskii
Publisher : Springer Science & Business Media
Page : 353 pages
File Size : 55,6 Mb
Release : 2011-09-20
Category : Mathematics
ISBN : 9783642232800

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Stochastic Stability of Differential Equations by Rafail Khasminskii Pdf

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 : Rafail Khasminskii
Publisher : Springer
Page : 342 pages
File Size : 48,8 Mb
Release : 2013-11-27
Category : Mathematics
ISBN : 364227028X

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Stochastic Stability of Differential Equations by Rafail Khasminskii Pdf

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 : Kai Liu
Publisher : Cambridge University Press
Page : 277 pages
File Size : 50,8 Mb
Release : 2019-05-02
Category : Mathematics
ISBN : 9781108705172

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Stochastic Stability of Differential Equations in Abstract Spaces by Kai Liu Pdf

Presents a unified treatment of stochastic differential equations in abstract, mainly Hilbert, spaces.

Author : R.Z. Has'minskii
Publisher : Springer
Page : 0 pages
File Size : 44,6 Mb
Release : 1981-01-14
Category : Mathematics
ISBN : 9400991215

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Stochastic stability of differential equations by R.Z. Has'minskii Pdf

I am very pleased to witness the printing of an English edition of this book by Noordhoff International Publishing. Since the date of the first Russian edition in 1969 there have appeared no less than two specialist texts devoted at least partly to the problems deal t wi th in the present book (Bunke [4] , Morozan [7]). There have also appeared a large number of research papers on our subject. Also worth mentioning is the monograph of Sagirov [1] containing ap plications of some of the results of this book to cosmology. In the hope of bringing the book somewhat more up to date we have written, jointly with M.B. Nevel'son, an Appendix contain ing an exposition of recent results. Also, we have in some places improved the original text of the book and have made some corrections. Among these changes, the following two are espe cially worth mentioning: A new version of Section 8.4, generaliz ing and simplifying the previous exposition, and a new presenta tion of Theorem 7.4.1 rendering correct the reference to this Theorem in Section 8.5.

Author : Kai Liu
Publisher : CRC Press
Page : 312 pages
File Size : 43,8 Mb
Release : 2005-08-23
Category : Mathematics
ISBN : 9781420034820

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Stability of Infinite Dimensional Stochastic Differential Equations with Applications by Kai Liu Pdf

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 : Xuerong Mao
Publisher : CRC Press
Page : 328 pages
File Size : 49,5 Mb
Release : 1994-05-02
Category : Mathematics
ISBN : 0824790804

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Exponential Stability of Stochastic Differential Equations by Xuerong Mao Pdf

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 : Leonid Shaikhet
Publisher : Springer Science & Business Media
Page : 352 pages
File Size : 52,8 Mb
Release : 2013-03-29
Category : Technology & Engineering
ISBN : 9783319001012

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Lyapunov Functionals and Stability of Stochastic Functional Differential Equations by Leonid Shaikhet Pdf

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 : Xuerong Mao
Publisher : Unknown
Page : 304 pages
File Size : 45,6 Mb
Release : 1991
Category : Semimartingales (Mathematics).
ISBN : CORNELL:31924059424022

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Stability of Stochastic Differential Equations with Respect to Semimartingales by Xuerong Mao Pdf

Author : X Mao
Publisher : Elsevier
Page : 440 pages
File Size : 46,7 Mb
Release : 2007-12-30
Category : Mathematics
ISBN : 9780857099402

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Stochastic Differential Equations and Applications by X Mao Pdf

This advanced undergraduate and graduate text has now been revised and updated to cover the basic principles and applications of various types of stochastic systems, with much on theory and applications not previously available in book form. The text is also useful as a reference source for pure and applied mathematicians, statisticians and probabilists, engineers in control and communications, and information scientists, physicists and economists. Has been revised and updated to cover the basic principles and applications of various types of stochastic systems Useful as a reference source for pure and applied mathematicians, statisticians and probabilists, engineers in control and communications, and information scientists, physicists and economists

Author : R. F. Curtain
Publisher : Springer
Page : 343 pages
File Size : 50,9 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540380009

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Stability of Stochastic Dynamical Systems by R. F. Curtain Pdf

Author : Leonid Shaikhet
Publisher : Springer Science & Business Media
Page : 374 pages
File Size : 47,6 Mb
Release : 2011-06-02
Category : Technology & Engineering
ISBN : 9780857296856

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Lyapunov Functionals and Stability of Stochastic Difference Equations by Leonid Shaikhet Pdf

Hereditary systems (or systems with either delay or after-effects) are widely used to model processes in physics, mechanics, control, economics and biology. An important element in their study is their stability. Stability conditions for difference equations with delay can be obtained using a Lyapunov functional. Lyapunov Functionals and Stability of Stochastic Difference Equations describes a general method of Lyapunov functional construction to investigate the stability of discrete- and continuous-time stochastic Volterra difference equations. The method allows the investigation of the degree to which the stability properties of differential equations are preserved in their difference analogues. The text is self-contained, beginning with basic definitions and the mathematical fundamentals of Lyapunov functional construction and moving on from particular to general stability results for stochastic difference equations with constant coefficients. Results are then discussed for stochastic difference equations of linear, nonlinear, delayed, discrete and continuous types. Examples are drawn from a variety of physical systems including inverted pendulum control, study of epidemic development, Nicholson’s blowflies equation and predator–prey relationships. Lyapunov Functionals and Stability of Stochastic Difference Equations is primarily addressed to experts in stability theory but will also be of use in the work of pure and computational mathematicians and researchers using the ideas of optimal control to study economic, mechanical and biological systems.

Author : Rangquan Wu
Publisher : Pitman Advanced Publishing Program
Page : 166 pages
File Size : 40,5 Mb
Release : 1985
Category : Stochastic differential equations
ISBN : UCAL:B4405677

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Stochastic Differential Equations by Rangquan Wu Pdf

Author : Xuerong Mao,Chenggui Yuan
Publisher : Imperial College Press
Page : 430 pages
File Size : 48,5 Mb
Release : 2006
Category : Mathematics
ISBN : 9781860947018

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Stochastic Differential Equations with Markovian Switching by Xuerong Mao,Chenggui Yuan Pdf

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 : Tobias Damm
Publisher : Springer Science & Business Media
Page : 228 pages
File Size : 45,5 Mb
Release : 2004-01-23
Category : Mathematics
ISBN : 3540205160

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Rational Matrix Equations in Stochastic Control by Tobias Damm Pdf

This book is the first comprehensive treatment of rational matrix equations in stochastic systems, including various aspects of the field, previously unpublished results and explicit examples. Topics include modelling with stochastic differential equations, stochastic stability, reformulation of stochastic control problems, analysis of the rational matrix equation and numerical solutions. Primarily a survey in character, this monograph is intended for researchers, graduate students and engineers in control theory and applied linear algebra.

Author : Leszek Gawarecki,Vidyadhar Mandrekar
Publisher : Springer Science & Business Media
Page : 300 pages
File Size : 49,7 Mb
Release : 2010-11-29
Category : Mathematics
ISBN : 9783642161940

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Stochastic Differential Equations in Infinite Dimensions by Leszek Gawarecki,Vidyadhar Mandrekar Pdf

The systematic study of existence, uniqueness, and properties of solutions to stochastic differential equations in infinite dimensions arising from practical problems characterizes this volume that is intended for graduate students and for pure and applied mathematicians, physicists, engineers, professionals working with mathematical models of finance. Major methods include compactness, coercivity, monotonicity, in a variety of set-ups. The authors emphasize the fundamental work of Gikhman and Skorokhod on the existence and uniqueness of solutions to stochastic differential equations and present its extension to infinite dimension. They also generalize the work of Khasminskii on stability and stationary distributions of solutions. New results, applications, and examples of stochastic partial differential equations are included. This clear and detailed presentation gives the basics of the infinite dimensional version of the classic books of Gikhman and Skorokhod and of Khasminskii in one concise volume that covers the main topics in infinite dimensional stochastic PDE’s. By appropriate selection of material, the volume can be adapted for a 1- or 2-semester course, and can prepare the reader for research in this rapidly expanding area.