Statistics of Random Processes II: Applications / Edition 2by A.B. Aries, Robert S. Liptser, Albert N. Shiryaev
Pub. Date: 12/12/2000
Publisher: Springer Berlin Heidelberg
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, shastic differential… See more details below
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, shastic differential equations, the absolute continuity of probability measures for diffusion and Ito processes, elements of shastic 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.
- Springer Berlin Heidelberg
- Publication date:
- Stochastic Modelling and Applied Probability Series, #6
- Edition description:
- 2nd rev. and exp. ed. 2001
- Product dimensions:
- 6.10(w) x 9.25(h) x 0.36(d)
Table of Contents
11. Conditionally Gaussian Processes.- 12. Optimal Nonlinear Filtering: Interpolation and Extrapolation of Components of Conditionally Gaussian Processes.- 13. Conditionally Gaussian Sequences: Filtering and Related Problems.- 14. Application of Filtering Equations to Problems of Statistics of Random Sequences.- 15. Linear Estimation of Random Processes.- 16. Application of Optimal Nonlinear Filtering Equations to some Problems in Control Theory and Estimation Theory.- 17. Parameter Estimation and Testing of Statistical Hypotheses for Diffusion-Type Processes.- 18. Random Point Processes: Stieltjes Shastic Integrals.- 19. The Structure of Local Martingales, Absolute Continuity of Measures for Point Processes, and Filtering.- 20. Asymptotically Optimal Filtering.
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