Stochastic Stability Of Differential Equations
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Stochastic Stability Of Differential Equations
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Author : Rafail Khasminskii
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-09-20
Stochastic Stability Of Differential Equations written by Rafail Khasminskii and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-20 with Mathematics categories.
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.
Stochastic Stability Of Differential Equations
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Author : Rafail Khasminskii
language : en
Publisher: Springer
Release Date : 2013-11-27
Stochastic Stability Of Differential Equations written by Rafail Khasminskii and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-27 with Mathematics categories.
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.
Stochastic Stability Of Differential Equations
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Author : Rafail Khasminskii
language : en
Publisher: Springer
Release Date : 2011-09-25
Stochastic Stability Of Differential Equations written by Rafail Khasminskii and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-25 with Mathematics categories.
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.
Lyapunov Functionals And Stability Of Stochastic Functional Differential Equations
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Author : Leonid Shaikhet
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-29
Lyapunov Functionals And Stability Of Stochastic Functional Differential Equations written by Leonid Shaikhet and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-29 with Technology & Engineering categories.
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.
Exponential Stability Of Stochastic Differential Equations
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Author : Xuerong Mao
language : en
Publisher: CRC Press
Release Date : 1994-05-02
Exponential Stability Of Stochastic Differential Equations written by Xuerong Mao and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-05-02 with Mathematics categories.
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.
Lyapunov Functionals And Stability Of Stochastic Difference Equations
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Author : Leonid Shaikhet
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-06-02
Lyapunov Functionals And Stability Of Stochastic Difference Equations written by Leonid Shaikhet and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-02 with Technology & Engineering categories.
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.
Stochastic Stability Of Differential Equations
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Author : R.Z. Has'minskii
language : en
Publisher: Springer
Release Date : 1981-01-14
Stochastic Stability Of Differential Equations written by R.Z. Has'minskii and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981-01-14 with Mathematics categories.
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.
Stochastic Differential Equations And Applications
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Author : X Mao
language : en
Publisher: Elsevier
Release Date : 2007-12-30
Stochastic Differential Equations And Applications written by X Mao and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-30 with Mathematics categories.
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
Stochastic Differential Equations With Markovian Switching
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Author : Xuerong Mao
language : en
Publisher: Imperial College Press
Release Date : 2006
Stochastic Differential Equations With Markovian Switching written by Xuerong Mao and has been published by Imperial College Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
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.
Stochastic Stability Of Differential Equations
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Author : HAS'MINSKII.
language : en
Publisher:
Release Date :
Stochastic Stability Of Differential Equations written by HAS'MINSKII. and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.