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

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

by Robert Liptser, Albert N. Shiryaev
     
 

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ISBN-10: 3540639292

ISBN-13: 9783540639299

Pub. Date: 12/12/2000

Publisher: Springer Berlin Heidelberg

The subject of these two volumes is non-linear filtering (prediction a nd smoothing) theory and its application to the problem of optimal est imation, control with incomplete data, information theory, and sequent ial testing of hypothesis. The book is not only addressed to mathemati cians but should also serve the interests of other scientists who appl y

Overview

The subject of these two volumes is non-linear filtering (prediction a nd smoothing) theory and its application to the problem of optimal est imation, control with incomplete data, information theory, and sequent ial testing of hypothesis. The book is not only addressed to mathemati cians but should also serve the interests of other scientists who appl y probabilistic and statistical methods in their work. The theory of m artingales presented in the book has an independent interest in connec tion with problems from financial mathematics.

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:
6.14(w) x 9.21(h) x 0.04(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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