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140122 ||| eng |
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|a 9783662130438
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| 100 |
1 |
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|a Liptser, Robert S.
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| 245 |
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|a Statistics of Random Processes
|h Elektronische Ressource
|b I. General Theory
|c by Robert S. Liptser, Albert N. Shiryaev
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| 250 |
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|a 2nd ed. 2001
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| 260 |
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|a Berlin, Heidelberg
|b Springer Berlin Heidelberg
|c 2001, 2001
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| 300 |
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|a XV, 427 p
|b online resource
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| 505 |
0 |
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|a 1. Essentials of Probability Theory and Mathematical Statistics -- 2. Martingales and Related Processes: Discrete Time -- 3. Martingales and Related Processes: Continuous Time -- 4. The Wiener Process, the Stochastic Integral over the Wiener Process, and Stochastic Differential Equations -- 5. Square Integrable Martingales and Structure of the Functionals on a Wiener Process -- 6. Nonnegative Supermartingales and Martingales, and the Girsanov Theorem -- 7. Absolute Continuity of Measures corresponding to the Itô Processes and Processes of the Diffusion Type -- 8. General Equations of Optimal Nonlinear Filtering, Interpolation and Extrapolation of Partially Observable Random Processes -- 9. Optimal Filtering, Interpolation and Extrapolation of Markov Processes with a Countable Number of States -- 10. Optimal Linear Nonstationary Filtering
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| 653 |
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|a Statistical Theory and Methods
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| 653 |
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|a Dynamical Systems
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| 653 |
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|a Statistics
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| 653 |
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|a Probability Theory
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| 653 |
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|a Dynamical systems
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| 653 |
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|a Probabilities
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| 700 |
1 |
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|a Shiryaev, Albert N.
|e [author]
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| 041 |
0 |
7 |
|a eng
|2 ISO 639-2
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| 989 |
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|b SBA
|a Springer Book Archives -2004
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| 490 |
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|a Stochastic Modelling and Applied Probability
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| 028 |
5 |
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|a 10.1007/978-3-662-13043-8
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| 856 |
4 |
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|u https://doi.org/10.1007/978-3-662-13043-8?nosfx=y
|x Verlag
|3 Volltext
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| 082 |
0 |
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|a 515.39
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| 520 |
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|a 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 asa new chapter devoted to asymptotically optimal filtering under diffusion approximation. Moreover, in each chapter a comment is added about the progress of recent years
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