Statistics of Random Processes | Buch

Cover: 9783540639299 | Statistics of Random Processes | I. General Theory | Liptser (u. a.)

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Sprache: Englisch

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Beschreibung

At the end of 1960s and the beginning of 1970s, when the Russian version of this book was written, the 'general theory of random processes' did not operate widely with such notions as semimartingale, stochastic integral with respect to semimartingale, the ItO formula for semimartingales, etc. At that time in stochastic calculus (theory of martingales), the main object was the square integrable martingale. In a short time, this theory was applied to such areas as nonlinear filtering, optimal stochastic control, statistics for diffusion type processes. In the first edition of these volumes, the stochastic calculus, based on square integrable martingale theory, was presented in detail with the proof of the Doob-Meyer decomposition for submartingales and the description of a structure for stochastic integrals. In the first volume ('General Theory') these results were used for a presentation of further important facts such as the Girsanov theorem and its generalizations, theorems on the innovation pro cesses, structure of the densities (Radon-Nikodym derivatives) for absolutely continuous measures being distributions of diffusion and Itô-type processes, and existence theorems for weak and strong solutions of stochastic differential equations. All the results and facts mentioned above have played a key role in the derivation of 'general equations' for nonlinear filtering, prediction, and smoothing of random processes.

Zusammenfassung

In the second edition, two new subsections devoted to the Kalman filter under wrong initial conditions, and a new chapter on asymptotically optimal filtering under diffusion approximation have been added

In each chapter a comment is added about the progress of recent years

Inhaltsverzeichnis

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.

Details

Erscheinungsjahr:	2000
Fachbereich:	Wahrscheinlichkeitstheorie
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Inhalt:	xv 427 S.
ISBN-13:	9783540639299
ISBN-10:	3540639292
Sprache:	Englisch
Einband:	Gebunden
Autor:	Liptser, Robert S. Shiryaev, Albert N.
Übersetzung:	Aries, B.
Auflage:	Second Edition 2001
Hersteller:	Springer-Verlag GmbH Springer Berlin Heidelberg
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	241 x 160 x 29 mm
Von/Mit:	Robert S. Liptser (u. a.)
Erscheinungsdatum:	06.11.2000
Gewicht:	0,834 kg

Artikel-ID: 106520542

Zusammenfassung

In each chapter a comment is added about the progress of recent years

Inhaltsverzeichnis

Details

Erscheinungsjahr:	2000
Fachbereich:	Wahrscheinlichkeitstheorie
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Inhalt:	xv 427 S.
ISBN-13:	9783540639299
ISBN-10:	3540639292
Sprache:	Englisch
Einband:	Gebunden
Autor:	Liptser, Robert S. Shiryaev, Albert N.
Übersetzung:	Aries, B.
Auflage:	Second Edition 2001
Hersteller:	Springer-Verlag GmbH Springer Berlin Heidelberg
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	241 x 160 x 29 mm
Von/Mit:	Robert S. Liptser (u. a.)
Erscheinungsdatum:	06.11.2000
Gewicht:	0,834 kg