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Shaikhet, Leonid.

Lyapunov Functionals and Stability of Stochastic Difference Equations [electronic resource] / by Leonid Shaikhet. - VI, 284p. 119 illus., 117 illus. in color. online resource.

Lyapunov-type Theorems and Procedure for Lyapunov Functional Construction -- Illustrative Example -- Linear Equations with Stationary Coefficients -- Linear Equations with Nonstationary Coefficients -- Some Peculiarities of the Method -- Systems of Linear Equations with Varying Delays -- Nonlinear Systems -- Volterra Equations of the Second Type -- Difference Equations with Continuous Time -- Difference Equations as Difference Analogues of Differential Equations.

á 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 Lyapunov functionals. Lyapunov Functionals and Stability of Stochastic Difference Equations describes the general method of Lyapunov functionals 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 functionals 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 and biological systems including inverted pendulum control, 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. __________________________________________________________________________

ISBN: 9780857296856 99780857296856

Subjects--Topical Terms:
Engineering.
Engineering.
Control.
DIFFERENCE AND FUNCTIONAL EQUATIONS
FUNTIONAL EQUATIONS
MATHEMATICAL OPTIMIZATION
CALCULUS OF VARIATIONS AND OPTICALCONTROL, OBTIMIZATION
PROBABILITY TEORY AND STOCHASTIC PROCESSES
DISTRIBUTION (PROBABILITY THEORY)
MATHEMATICAL AND COMPUTATIONAL BIOLOGY
VIBRATION
VIBRATION

Dewey Class. No.: 629.8 / 223