000			03832nam a22005055i 4500
001			978-0-85729-685-6
003			DE-He213
005			20140220083714.0
007			cr nn 008mamaa
008			110601s2011 xxk| s |||| 0|eng d
020			_a9780857296856 _9978-0-85729-685-6
024	7		_a10.1007/978-0-85729-685-6 _2doi
050		4	_aTJ212-225
072		7	_aTJFM _2bicssc
072		7	_aTEC004000 _2bisacsh
082	0	4	_a629.8 _223
100	1		_aShaikhet, Leonid. _eauthor.
245	1	0	_aLyapunov Functionals and Stability of Stochastic Difference Equations _h[electronic resource] / _cby Leonid Shaikhet.
264		1	_aLondon : _bSpringer London, _c2011.
300			_aVI, 284p. 119 illus., 117 illus. in color. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
505	0		_aLyapunov-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.
520			_a  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. __________________________________________________________________________
650		0	_aEngineering.
650		0	_aFunctional equations.
650		0	_aMathematical optimization.
650		0	_aDistribution (Probability theory).
650		0	_aVibration.
650	1	4	_aEngineering.
650	2	4	_aControl.
650	2	4	_aDifference and Functional Equations.
650	2	4	_aCalculus of Variations and Optimal Control; Optimization.
650	2	4	_aMathematical and Computational Biology.
650	2	4	_aProbability Theory and Stochastic Processes.
650	2	4	_aVibration, Dynamical Systems, Control.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780857296849
856	4	0	_uhttp://dx.doi.org/10.1007/978-0-85729-685-6
912			_aZDB-2-ENG
999			_c105257 _d105257