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Although three decades have passed since first publication of this book reprinted now as a result of popular demand, the content remains up-to-date and interesting for many researchers as is shown by the many references to it in current publications. The "ground floor" of Optimal Stopping Theory was constructed by A.Wald in his sequential analysis in connection with the testing of statistical hypotheses by non-traditional (sequential) methods. It was later discovered that these methods have, in idea, a close connection to the general theory of stochastic optimization for random processes. The area of application of the Optimal Stopping Theory is very broad. It is sufficient at this point to emphasise that its methods are well tailored to the study of American (-type) options (in mathematics of finance and financial engineering), where a buyer has the freedom to exercise an option at any stopping time. In this book, the general theory of the construction of optimal stopping policies is developed for the case of Markov processes in discrete and continuous time. One chapter is devoted specially to the applications that address problems of the testing of statistical hypotheses, and quickest detection of the time of change of the probability characteristics of the observable processes. The author, A.N.Shiryaev, is one of the leading experts of the field and gives an authoritative treatment of a subject that, 30 years after original publication of this book, is proving increasingly important.
Optimal stopping (Mathematical statistics) --- Sequential analysis. --- Mathematical statistics --- Statistical decision --- Stopping, Optimal (Mathematical statistics) --- Sequential analysis --- Distribution (Probability theory. --- Statistics. --- Probability Theory and Stochastic Processes. --- Statistics for Business, Management, Economics, Finance, Insurance. --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Mathematics --- Econometrics --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Probabilities. --- Statistics . --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Risk
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Stochastic processes --- Sequential analysis --- Optimal stopping (Mathematical statistics) --- Dualité, théorie de la (Mathématiques) --- 519.216 --- Mathematical statistics --- Statistical decision --- Stopping, Optimal (Mathematical statistics) --- Stochastic processes in general. Prediction theory. Stopping times. Martingales --- Sequential analysis. --- Optimal stopping (Mathematical statistics). --- 519.216 Stochastic processes in general. Prediction theory. Stopping times. Martingales --- Arrêt optimal (Statistique mathématique) --- Dualité, théorie de la (Mathématiques) --- Arrêt optimal (Statistique mathématique)
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Stochastic processes --- Gauss, Carl Friedrich --- Gaussian processes --- Processus gaussiens --- 519.216 --- #WWIS:STAT --- Distribution (Probability theory) --- Stochastic processes in general. Prediction theory. Stopping times. Martingales --- Gaussian processes. --- 519.216 Stochastic processes in general. Prediction theory. Stopping times. Martingales --- Probabilités. --- Probabilities --- Markov, Processus de --- Markov processes --- Probabilités.
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The subject of these two volumes is non-linear filtering (prediction and smoothing) theory and its application to the problem of optimal estimation, control with incomplete data, information theory, and sequential testing of hypothesis. The required mathematical background is presented in the first volume: the theory of martingales, stochastic differential equations, the absolute continuity of probability measures for diffusion and Ito processes, elements of stochastic calculus for counting processes. The book is not only addressed to mathematicians but should also serve the interests of other scientists who apply probabilistic and statistical methods in their work. The theory of martingales presented in the book has an independent interest in connection with problems from financial mathematics. In the second edition, the authors have made numerous corrections, updating every chapter, adding two new subsections devoted to the Kalman filter under wrong initial conditions, as well as a new chapter devoted to asymptotically optimal filtering under diffusion approximation. Moreover, in each chapter a comment is added about the progress of recent years.
Processus stochastiques --- Statistique mathématique --- Stochastic processes --- Mathematical statistics --- 519.2 --- 519.2 Probability. Mathematical statistics --- Probability. Mathematical statistics --- Mathematics --- Statistical inference --- Statistics, Mathematical --- Statistics --- Probabilities --- Sampling (Statistics) --- Random processes --- Statistical methods --- Probabilities. --- Statistics . --- Probability Theory and Stochastic Processes. --- Statistical Theory and Methods. --- Statistical analysis --- Statistical data --- Statistical science --- Econometrics --- Probability --- Combinations --- Chance --- Least squares --- Risk --- Dynamics. --- Ergodic theory. --- Dynamical Systems and Ergodic Theory. --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics
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Control theory --- Diffusion processes --- Théorie de la commande --- Processus de diffusion
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Stochastic processes --- Mathematical statistics --- 519.246 --- #WWIS:IBM/STAT --- Statistics of stochastic processes. Estimation of stochastic processes. Hypothesis testing. Statistics of point processes. Time series analysis. Auto-correlation. Regression --- 519.246 Statistics of stochastic processes. Estimation of stochastic processes. Hypothesis testing. Statistics of point processes. Time series analysis. Auto-correlation. Regression --- Mathematics --- Statistical inference --- Statistics, Mathematical --- Statistics --- Probabilities --- Sampling (Statistics) --- Random processes --- Statistical methods --- Stochastic processes. --- Mathematical statistics. --- Statistique mathématique --- Processus stochastiques
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