Statistics of Random Processes: I. General Theory / Edition 2

Statistics of Random Processes: I. General Theory / Edition 2

by Robert Liptser, B. Aries, Albert N. Shiryaev
     
 

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

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Overview

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.

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Product Details

ISBN-13:
9783540639299
Publisher:
Springer Berlin Heidelberg
Publication date:
12/12/2000
Series:
Stochastic Modelling and Applied Probability Series, #5
Edition description:
2nd rev. and exp. ed. 2001
Pages:
427
Product dimensions:
9.21(w) x 6.14(h) x 1.00(d)

Related Subjects

Table of Contents

Essentials of probability theory and mathematical statistics.- Martingales and related processes.- Martingales and supermartingales: continuous time.- The Wiener process, the shastic integral over the Wiener process, and shastic 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.

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