Statistics of Random Processes : I. General Theory /
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...
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| Format: | eBook |
| Language: | English |
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Berlin, Heidelberg :
Springer Berlin Heidelberg,
2001.
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| Edition: | Second, rev. and Expanded edition. |
| Series: | Applications of Mathematics, Stochastic Modelling and Applied Probability ;
5. |
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| Online Access: | Connect to the full text of this electronic book |
Table of Contents:
- Essentials of probability theory and mathematical statistics
- Martingales and related processes
- Martingales and supermartingales: continuous time
- The Wiener process, the stochastic integral over the Wiener process, and stochastic differential equations
- Square integrable martingales, and structure of the functionals on a Wiener process
- Nonnegative supermartingales and martingales, and the Girsanovs theorem
- Absolute continuity of measures corresponding to the Ito processes and processes of diffusion type
- General equations of optimal nonlinear filtering, interpolation and extrapolation of partially observable random processes
- Optimal filtering, interpolation and extrapolation of Markov processes with countable number of states
- Optimal linear nonstationary filtering.