عنوان

Statistics of Random Processes

(Number (ISBN

9783642083662

(Number (ISBN

9783662130438

Number

b407057

Title Proper

Statistics of Random Processes

General Material Designation

[Book]

Other Title Information

I. General Theory /

First Statement of Responsibility

by Robert S. Liptser, Albert N. Shiryaev.

Edition Statement

Second, Revised and Expanded Edition.

Place of Publication, Distribution, etc.

Berlin, Heidelberg :

Name of Publisher, Distributor, etc.

Imprint: Springer,

Date of Publication, Distribution, etc.

2001.

Series Title

Applications of Mathematics, Stochastic Modelling and Applied Probability,

Volume Designation

5

ISSN of Series

0172-4568 ;

Text of Note

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.

0

Text of Note

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, stochastic differential equations, the absolute continuity of probability measures for diffusion and Ito processes, elements of stochastic 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.

International Standard Book Number

9783642083662

Title

Springer eBooks

Distribution (Probability theory).

Mathematical statistics.

Mathematics.

Liptser, Robert S.

Shiri︠a︡ev, Alʹbert Nikolaevich.

SpringerLink (Online service)

Date of Transaction

20190307162300.0

Electronic name

[Book]

Y