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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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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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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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