Lyapunov Functionals and Stability of Stochastic Difference Equations

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 ...

Lyapunov Functionals and Stability of Stochastic Difference Equations

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.

More Books:

Lyapunov Functionals and Stability of Stochastic Difference Equations
Language: en
Pages: 370
Authors: Leonid Shaikhet
Categories: Technology & Engineering
Type: BOOK - Published: 2011-06-02 - Publisher: Springer Science & Business Media

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
Lyapunov Functionals and Stability of Stochastic Functional Differential Equations
Language: en
Pages: 342
Authors: Leonid Shaikhet
Categories: Technology & Engineering
Type: BOOK - Published: 2013-03-29 - Publisher: Springer Science & Business Media

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
Optimal Control of Stochastic Difference Volterra Equations
Language: en
Pages: 220
Authors: Leonid Shaikhet
Categories: Technology & Engineering
Type: BOOK - Published: 2014-11-27 - Publisher: Springer

This book showcases a subclass of hereditary systems, that is, systems with behaviour depending not only on their current state but also on their past history; it is an introduction to the mathematical theory of optimal control for stochastic difference Volterra equations of neutral type. As such, it will be
Energy Research Abstracts
Language: en
Pages:
Authors: Leonid Shaikhet
Categories: Power resources
Type: BOOK - Published: 1993 - Publisher:

Semiannual, with semiannual and annual indexes. References to all scientific and technical literature coming from DOE, its laboratories, energy centers, and contractors. Includes all works deriving from DOE, other related government-sponsored information, and foreign nonnuclear information. Arranged under 39 categories, e.g., Biomedical sciences, basic studies; Biomedical sciences, applied studies; Health
Stochastic Differential Equations and Applications
Language: en
Pages: 440
Authors: X Mao
Categories: Mathematics
Type: BOOK - Published: 2007-12-30 - Publisher: Elsevier

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