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Focusing on discrete-time-scale Markov chains, the contents of this book are an outgrowth of some of the authors' recent research. The motivation stems from existing and emerging applications in optimization and control of complex hybrid Markovian systems in manufacturing, wireless communication, and financial engineering. Much effort in this book is devoted to designing system models arising from these applications, analyzing them via analytic and probabilistic techniques, and developing feasible computational algorithms so as to reduce the inherent complexity. This book presents results including asymptotic expansions of probability vectors, structural properties of occupation measures, exponential bounds, aggregation and decomposition and associated limit processes, and interface of discrete-time and continuous-time systems. One of the salient features is that it contains a diverse range of applications on filtering, estimation, control, optimization, and Markov decision processes, and financial engineering. This book will be an important reference for researchers in the areas of applied probability, control theory, operations research, as well as for practitioners who use optimization techniques. Part of the book can also be used in a graduate course of applied probability, stochastic processes, and applications.

Markov processes. --- Stochastic processes. --- Random processes --- Probabilities --- Analysis, Markov --- Chains, Markov --- Markoff processes --- Markov analysis --- Markov chains --- Markov models --- Models, Markov --- Processes, Markov --- Stochastic processes --- Distribution (Probability theory. --- Operations research. --- Mathematics. --- Probability Theory and Stochastic Processes. --- Control, Robotics, Mechatronics. --- Operations Research/Decision Theory. --- Applications of Mathematics. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Math --- Science --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Probabilities. --- Control engineering. --- Robotics. --- Mechatronics. --- Decision making. --- Applied mathematics. --- Engineering mathematics. --- Engineering --- Engineering analysis --- Mathematical analysis --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Control engineering --- Control equipment --- Control theory --- Engineering instruments --- Automation --- Programmable controllers --- Mechanical engineering --- Microelectronics --- Microelectromechanical systems --- Machine theory --- Deciding --- Decision (Psychology) --- Decision analysis --- Decision processes --- Making decisions --- Management --- Management decisions --- Choice (Psychology) --- Problem solving --- Decision making

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This volume collects papers, based on invited talks given at the IMA workshop in Modeling, Stochastic Control, Optimization, and Related Applications, held at the Institute for Mathematics and Its Applications, University of Minnesota, during May and June, 2018. There were four week-long workshops during the conference. They are (1) stochastic control, computation methods, and applications, (2) queueing theory and networked systems, (3) ecological and biological applications, and (4) finance and economics applications. For broader impacts, researchers from different fields covering both theoretically oriented and application intensive areas were invited to participate in the conference. It brought together researchers from multi-disciplinary communities in applied mathematics, applied probability, engineering, biology, ecology, and networked science, to review, and substantially update most recent progress. As an archive, this volume presents some of the highlights of the workshops, and collect papers covering a broad range of topics.

Stochastic control theory. --- Distribution (Probability theory. --- Mathematical optimization. --- Probability Theory and Stochastic Processes. --- Calculus of Variations and Optimal Control; Optimization. --- Continuous Optimization. --- Mathematical Modeling and Industrial Mathematics. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Probabilities. --- Calculus of variations. --- Mathematical models. --- Models, Mathematical --- Isoperimetrical problems --- Variations, Calculus of --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk

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This revised and expanded second edition presents a thorough development of the modern theory of stochastic approximation or recursive stochastic algorithms for both constrained and unconstrained problems. There is a complete development of both probability one and weak convergence methods for very general noise processes. The proofs of convergence use the ODE method, the most powerful to date. The assumptions and proof methods are designed to cover the needs of recent applications. The development proceeds from simple to complex problems, allowing the underlying ideas to be more easily understood. Rate of convergence, iterate averaging, high-dimensional problems, stability-ODE methods, two time scale, asynchronous and decentralized algorithms, state-dependent noise, stability methods for correlated noise, perturbed test function methods, and large deviations methods are covered. Many motivating examples from learning theory, ergodic cost problems for discrete event systems, wireless communications, adaptive control, signal processing, and elsewhere illustrate the applications of the theory.

Distribution (Probability theory. --- Artificial intelligence. --- Mathematics. --- Algorithms. --- Probability Theory and Stochastic Processes. --- Artificial Intelligence. --- Approximations and Expansions. --- Applications of Mathematics. --- Probabilities. --- Approximation theory. --- Applied mathematics. --- Engineering mathematics. --- Algorism --- Algebra --- Arithmetic --- Engineering --- Engineering analysis --- Mathematical analysis --- Theory of approximation --- Functional analysis --- Functions --- Polynomials --- Chebyshev systems --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Bionics --- Cognitive science --- Digital computer simulation --- Electronic data processing --- Logic machines --- Machine theory --- Self-organizing systems --- Simulation methods --- Fifth generation computers --- Neural computers --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Foundations --- Stochastic approximation. --- Recursive functions. --- Functions, Recursive --- Algorithms --- Logic, Symbolic and mathematical --- Number theory --- Recursion theory --- Decidability (Mathematical logic) --- Approximation theory --- Stochastic processes

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Double taxation --- Income tax --- Double taxation --- Income tax --- Double taxation --- Income tax --- Law and legislation --- Law and legislation --- Law and legislation

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Social security taxes --- Social security --- Law and legislation --- Law and legislation