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Evolution of Systems in Random Media is an innovative, application-oriented text that explores stochastic models of evolutionary stochastic systems in random media. Specially designed for researchers and practitioners who do not have a background in random evolutions, the book allows non-experts to explore the potential information and applications that random evolutions can provide.
Table of Contents
Introduction The Martingale Problem and Weak Convergence in Banach Space Random Processes and Martingales in Banach Space Operator Semi-Groups Markov Processes: Martingale Characterization Weak Convergence Martingale Problem in Banach Space Markov Renewal Processes Semi-Markov Processes Singular Perturbed Problems Perturbation of Reducible-Invertible Operators Phase Merging of Semi-Markov Processes Semi-Markov Random Evolutions Definition and Classification of Random Evolutions Stochastic Models of Systems Inhomogeneous Semi-Markov Random Evolutions Weak Convergence of Random Evolutions Relative Compactness of Random Evolutions Limiting Evolutions in Averaging and Diffusion Approximation Schemes Uniqueness of the Solution of the Martingale Problem Averaging and Diffusion Approximation of Random Evolution in Reducible Random Media Averaging of Stochastic Systems in Semi-Markov Random Media Compacts in Banach Spaces Traffic Processes Impulse Traffic Processes Additive Functionals Stochastic Differential Equations U-Statistical Processes Random Evolutions on Lie Groups Oscillations of a Harmonic Oscillator Waves in Conductors and Beams Diffusion Approximation of Stochastic Systems Traffic Processes Impulse Traffic Processes Additive Functionals U-Statistical Processes Random Motions on Lie Groups Normal Deviations of Semi-Markov Random Evolutions Random Evolution in Ergodic Media Stochastic Systems Random Evolution in Reducible Media Evolutionary Stochastic Systems in Reducible Media Rates of Convergence in the Limit Theorems for Random Evolutions Averaging Schemes for Random Evolutions Diffusion Approximation Scheme for Random Evolutions Averaging Scheme for Evolutionary Stochastic Systems in Random Media Diffusion Approximation Scheme for Evolutionary Stochastic Systems in Random Media Stability of Stochastic Systems Traffic Process in the Averaging Scheme Traffic Process in the Diffusion Approximation Scheme Impulse Traffic Process in the Averaging Scheme Impulse Traffic Process in the Diffusion Approximation Scheme Control of Evolutionary Stochastic Systems in Random Media Functionals of Uncontrolled Processes Cost Functionals Optimal Stochastic Control Bibliography Subject Index
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CHOICE – Outstanding Academic Title – Award Winner
CHOICE – 2018 Outstanding Academic Title – Award Winner
Shingo Research and Professional Publication Award Winner
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