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Cover: 9783540639282 | Statistics of Random Processes II | Applications | Liptser (u. a.)
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Statistics of Random Processes II
Applications
Buch von Robert S. Liptser (u. a.)
Sprache: Englisch

149,79 €*

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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 ItO-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.
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 ItO-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

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

Inhaltsverzeichnis
11. Conditionally Gaussian Processes.- 12. Optimal Nonlinear Filtering: Interpolation and Extrapolation of Components of Conditionally Gaussian Processes.- 13. Conditionally Gaussian Sequences: Filtering and Related Problems.- 14. Application of Filtering Equations to Problems of Statistics of Random Sequences.- 15. Linear Estimation of Random Processes.- 16. Application of Optimal Nonlinear Filtering Equations to some Problems in Control Theory and Estimation Theory.- 17. Parameter Estimation and Testing of Statistical Hypotheses for Diffusion-Type Processes.- 18. Random Point Processes: Stieltjes Stochastic Integrals.- 19. The Structure of Local Martingales, Absolute Continuity of Measures for Point Processes, and Filtering.- 20. Asymptotically Optimal Filtering.
Details
Erscheinungsjahr: 2000
Fachbereich: Wahrscheinlichkeitstheorie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Reihe: Stochastic Modelling and Applied Probability
Inhalt: xv
402 S.
ISBN-13: 9783540639282
ISBN-10: 3540639284
Sprache: Englisch
Herstellernummer: 10640137
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Liptser, Robert S.
Shiryaev, Albert N.
Übersetzung: Aries, A. B.
Auflage: 2nd revidierte and exp. ed. 2001
Hersteller: Springer-Verlag GmbH
Springer Berlin Heidelberg
Stochastic Modelling and Applied Probability
Maße: 241 x 160 x 28 mm
Von/Mit: Robert S. Liptser (u. a.)
Erscheinungsdatum: 06.11.2000
Gewicht: 0,799 kg
Artikel-ID: 102288492
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

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

Inhaltsverzeichnis
11. Conditionally Gaussian Processes.- 12. Optimal Nonlinear Filtering: Interpolation and Extrapolation of Components of Conditionally Gaussian Processes.- 13. Conditionally Gaussian Sequences: Filtering and Related Problems.- 14. Application of Filtering Equations to Problems of Statistics of Random Sequences.- 15. Linear Estimation of Random Processes.- 16. Application of Optimal Nonlinear Filtering Equations to some Problems in Control Theory and Estimation Theory.- 17. Parameter Estimation and Testing of Statistical Hypotheses for Diffusion-Type Processes.- 18. Random Point Processes: Stieltjes Stochastic Integrals.- 19. The Structure of Local Martingales, Absolute Continuity of Measures for Point Processes, and Filtering.- 20. Asymptotically Optimal Filtering.
Details
Erscheinungsjahr: 2000
Fachbereich: Wahrscheinlichkeitstheorie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Reihe: Stochastic Modelling and Applied Probability
Inhalt: xv
402 S.
ISBN-13: 9783540639282
ISBN-10: 3540639284
Sprache: Englisch
Herstellernummer: 10640137
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Liptser, Robert S.
Shiryaev, Albert N.
Übersetzung: Aries, A. B.
Auflage: 2nd revidierte and exp. ed. 2001
Hersteller: Springer-Verlag GmbH
Springer Berlin Heidelberg
Stochastic Modelling and Applied Probability
Maße: 241 x 160 x 28 mm
Von/Mit: Robert S. Liptser (u. a.)
Erscheinungsdatum: 06.11.2000
Gewicht: 0,799 kg
Artikel-ID: 102288492
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