Statistics of Random Processes
Subtitle: II. Applications
By: by Robert S. Liptser, Albert N. Shiryaev
Contributors: Shiryaev, Albert N.
Edition: Second, Revised and Expanded Edition.
Series: Stochastic Modelling and Applied Probability -- 6; Stochastic Modelling and Applied Probability -- 6
Publisher: Springer Berlin Heidelberg
Published: 2001
Place of publication: Berlin, Heidelberg
Language: eng
Format: [electronic resource] :
Number of pages: 402
ISBN-13: 9783642083655; 9783662100288
Subjects: Mathematics; Distribution (Probability theory); Mathematical statistics
Description: 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.
Notes: Online full text is restricted to subscribers.

Also available in print.

Mode of access: World Wide Web.
Table of contents: title: Conditionally Gaussian processes; title: Optimal nonlinear filtering, interpolation, and extrapolation of components of conditionally Gaussian processes; title: Conditionally Gaussian sequences:filtering and related problems; title: Application of filtering equations to problems of statistics of random sequences; title: Linear Estimation of random processes; title: Application of optimal nonlinear filtering equations to some problems in control theory and information theory; title: Parameter estimation and testing of statistical hypotheses for diffusion type processes; title: Random point processes: Stieltjes stochastic integrals; title: The structure of local martingales, absolute continuity of measures for point processes, and filtering; title: Asymptotically optimal filtering.