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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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Bibliographic Details
Main Authors: Liptser, Robert S., Shiryaev, Albert N. (Author)
Format: eBook
Language:English
Published: Berlin, Heidelberg Springer Berlin Heidelberg 2001, 2001
Edition:2nd ed. 2001
Series:Stochastic Modelling and Applied Probability
Subjects:
Statistical Theory And Methods
Dynamical Systems
Statistics 
Probability Theory
Probabilities
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 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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