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Stochastic processes --- Markov processes. --- Markov, Processus de --- Markov processes --- 519.233 --- Analysis, Markov --- Chains, Markov --- Markoff processes --- Markov analysis --- Markov chains --- Markov models --- Models, Markov --- Processes, Markov

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Safety critical and high-integrity systems, such as industrial plants and economic systems, can be subject to abrupt changes - for instance, due to component or interconnection failure, sudden environment changes, etc. Combining probability and operator theory, Discrete-Time Markov Jump Linear Systems provides a unified and rigorous treatment of recent results for the control theory of discrete jump linear systems, which are used in these areas of application. The book is designed for experts in linear systems with Markov jump parameters, but is also of interest for specialists in stochastic control since it presents stochastic control problems for which an explicit solution is possible - making the book suitable for course use. Oswaldo Luiz do Valle Costa is Professor in the Department of Telecommunications and Control Engineering at the University of São Paulo, Marcelo Dutra Fragoso is Professor in the Department of Systems and Control at the National Laboratory for Scientific Computing - LNCC/MCT, Rio de Janeiro, and Ricardo Paulino Marques works in the Department of Telecommunications and Control Engineering at the University of São Paulo.

Stochastic control theory. --- Stochastic systems. --- Linear systems. --- Control theory. --- Markov processes. --- Analysis, Markov --- Chains, Markov --- Markoff processes --- Markov analysis --- Markov chains --- Markov models --- Models, Markov --- Processes, Markov --- Stochastic processes --- Dynamics --- Machine theory --- Systems, Linear --- Differential equations, Linear --- System theory --- Systems, Stochastic --- System analysis --- Control theory

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Probability theory arose originally in connection with games of chance and then for a long time it was used primarily to investigate the credibility of testimony of witnesses in the “ethical” sciences. Nevertheless, probability has become a very powerful mathematical tool in understanding those aspects of the world that cannot be described by deterministic laws. Probability has succeeded in ?nding strict determinate relationships where chance seemed to reign and so terming them “laws of chance” combining such contrasting - tions in the nomenclature appears to be quite justi?ed. This introductory chapter discusses such notions as determinism, chaos and randomness, p- dictibility and unpredictibility, some initial approaches to formalizing r- domness and it surveys certain problems that can be solved by probability theory. This will perhaps give one an idea to what extent the theory can - swer questions arising in speci?c random occurrences and the character of the answers provided by the theory. 1. 1 The Nature of Randomness The phrase “by chance” has no single meaning in ordinary language. For instance, it may mean unpremeditated, nonobligatory, unexpected, and so on. Its opposite sense is simpler: “not by chance” signi?es obliged to or bound to (happen). In philosophy, necessity counteracts randomness. Necessity signi?es conforming to law – it can be expressed by an exact law. The basic laws of mechanics, physics and astronomy can be formulated in terms of precise quantitativerelationswhichmustholdwithironcladnecessity.

Markov processes. --- Probabilities. --- Statistics. --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Statistics --- Analysis, Markov --- Chains, Markov --- Markoff processes --- Markov analysis --- Markov chains --- Markov models --- Models, Markov --- Processes, Markov --- Probability --- Statistical inference --- Mathematics. --- Probability Theory and Stochastic Processes. --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Stochastic processes --- Distribution (Probability theory. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities

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In this book, the functional inequalities are introduced to describe:(i) the spectrum of the generator: the essential and discrete spectrums, high order eigenvalues, the principle eigenvalue, and the spectral gap;(ii) the semigroup properties: the uniform intergrability, the compactness, the convergence rate, and the existence of density;(iii) the reference measure and the intrinsic metric: the concentration, the isoperimetic inequality, and the transportation cost inequality.

Ordered algebraic structures --- Stochastic processes --- Inequalities (Mathematics) --- Semigroups of operators. --- Dirichlet forms --- Markov processes --- Spectral theory (Mathematics) --- Inégalités (Mathématiques) --- Semi-groupes d'opérateurs --- Dirichlet, Formes de --- Markov, Processus de --- Spectre (Mathématiques) --- ELSEVIER-B EPUB-LIV-FT --- Semigroups. --- Markov processes. --- Functional analysis --- Hilbert space --- Measure theory --- Transformations (Mathematics) --- Analysis, Markov --- Chains, Markov --- Markoff processes --- Markov analysis --- Markov chains --- Markov models --- Models, Markov --- Processes, Markov --- Group theory --- Processes, Infinite

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Hidden Markov models have become a widely used class of statistical models with applications in diverse areas such as communications engineering, bioinformatics, finance and many more. This book is a comprehensive treatment of inference for hidden Markov models, including both algorithms and statistical theory. Topics range from filtering and smoothing of the hidden Markov chain to parameter estimation, Bayesian methods and estimation of the number of states. In a unified way the book covers both models with finite state spaces, which allow for exact algorithms for filtering, estimation etc. and models with continuous state spaces (also called state-space models) requiring approximate simulation-based algorithms that are also described in detail. Simulation in hidden Markov models is addressed in five different chapters that cover both Markov chain Monte Carlo and sequential Monte Carlo approaches. Many examples illustrate the algorithms and theory. The book also carefully treats Gaussian linear state-space models and their extensions and it contains a chapter on general Markov chain theory and probabilistic aspects of hidden Markov models. This volume will suit anybody with an interest in inference for stochastic processes, and it will be useful for researchers and practitioners in areas such as statistics, signal processing, communications engineering, control theory, econometrics, finance and more. The algorithmic parts of the book do not require an advanced mathematical background, while the more theoretical parts require knowledge of probability theory at the measure-theoretical level. Olivier Cappé is Researcher for the French National Center for Scientific Research (CNRS). He received the Ph.D. degree in 1993 from Ecole Nationale Supérieure des Télécommunications, Paris, France, where he is currently a Research Associate. Most of his current research concerns computational statistics and statistical learning. Eric Moulines is Professor at Ecole Nationale Supérieure des Télécommunications (ENST), Paris, France. He graduated from Ecole Polytechnique, France, in 1984 and received the Ph.D. degree from ENST in 1990. He has authored more than 150 papers in applied probability, mathematical statistics and signal processing. Tobias Rydén is Professor of Mathematical Statistics at Lund University, Sweden, where he also received his Ph.D. in 1993. His publications include papers ranging from statistical theory to algorithmic developments for hidden Markov models.

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. --- Mathematical statistics. --- Statistics. --- Computer simulation. --- Probability Theory and Stochastic Processes. --- Statistical Theory and Methods. --- Signal, Image and Speech Processing. --- Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences. --- Statistics for Business, Management, Economics, Finance, Insurance. --- Simulation and Modeling. --- Computer modeling --- Computer models --- Modeling, Computer --- Models, Computer --- Simulation, Computer --- Electromechanical analogies --- Mathematical models --- Simulation methods --- Model-integrated computing --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Mathematics --- Econometrics --- Statistical inference --- Statistics, Mathematical --- Statistics --- Sampling (Statistics) --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities. --- Statistics . --- Signal processing. --- Image processing. --- Speech processing systems. --- Probability --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Computational linguistics --- Electronic systems --- Information theory --- Modulation theory --- Oral communication --- Speech --- Telecommunication --- Singing voice synthesizers --- Pictorial data processing --- Picture processing --- Processing, Image --- Imaging systems --- Optical data processing --- Processing, Signal --- Information measurement --- Signal theory (Telecommunication)