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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 systemsUseful as

Stochastic differential equations. --- Differential equations --- Fokker-Planck equation

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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.

Stochastic differential equations. --- Differential equations, Partial. --- Distribution (Probability theory) --- Mathematics. --- Partial differential equations. --- Applied mathematics. --- Engineering mathematics. --- Economics, Mathematical. --- Probabilities. --- Probability Theory and Stochastic Processes. --- Partial Differential Equations. --- Quantitative Finance. --- Applications of Mathematics. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Partial differential equations --- Differential equations --- Fokker-Planck equation --- Distribution (Probability theory. --- Differential equations, partial. --- Finance. --- Math --- Science --- Funding --- Funds --- Economics --- Currency question --- Stochastic partial differential equations. --- Economics, Mathematical . --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Engineering --- Engineering analysis --- Mathematical analysis --- Mathematical economics --- Econometrics --- Methodology

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  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. __________________________________________________________________________.

Approximation theory. --- Differential equations, Hyperbolic. --- Lyapunov functions. --- Stochastic differential equations. --- Stochastic differential equations --- Lyapunov functions --- Engineering & Applied Sciences --- Mechanical Engineering --- Mathematics --- Physical Sciences & Mathematics --- Mechanical Engineering - General --- Mathematical Statistics --- Applied Mathematics --- Functions, Liapunov --- Liapunov functions --- Engineering. --- Difference equations. --- Functional equations. --- Calculus of variations. --- Probabilities. --- Biomathematics. --- Vibration. --- Dynamical systems. --- Dynamics. --- Control engineering. --- Control. --- Difference and Functional Equations. --- Calculus of Variations and Optimal Control; Optimization. --- Mathematical and Computational Biology. --- Probability Theory and Stochastic Processes. --- Vibration, Dynamical Systems, Control. --- Differential equations --- Fokker-Planck equation --- Mathematical optimization. --- Distribution (Probability theory. --- Control and Systems Theory. --- Cycles --- Mechanics --- Sound --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Equations, Functional --- Functional analysis --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Physics --- Statics --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Biology --- Isoperimetrical problems --- Variations, Calculus of --- Calculus of differences --- Differences, Calculus of --- Equations, Difference --- Control engineering --- Control equipment --- Control theory --- Engineering instruments --- Automation --- Programmable controllers