Statistics of Random Processes: I. General Theory

Liptser, Robert S. and Albert N. Shiryaev:

ISBN 10: 3540639292 / ISBN 13: 9783540639299

Editore: Berlin, Heidelberg, New York: Springer-Verlag, 2001

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XV, 427 Seiten, Stochastic Modelling and Applied Probability, Band 5. Zust: Gutes Exemplar. Schneller Versand und persönlicher Service - jedes Buch händisch geprüft und beschrieben - aus unserem Familienbetrieb seit über 25 Jahren. Eine Rechnung mit ausgewiesener Mehrwertsteuer liegt jeder unserer Lieferungen bei. Wir versenden mit der deutschen Post. Sprache: Englisch Gewicht in Gramm: 768 gebundene Ausgabe gebundene Ausgabe.

Codice articolo 493057

Dati bibliografici

• Titolo: Statistics of Random Processes: I. General Theory
• Editore: Berlin, Heidelberg, New York: Springer-Verlag
• Data di pubblicazione: 2001
• Lingua: Inglese
• ISBN 10: 3540639292
• ISBN 13: 9783540639299
• Rilegatura: Rilegato
• Edizione: Second, Revised and Expanded Edition.
• Condizione: Sehr gut
• Peso: 768 grammi
• Cataloghi dei venditori:
  • Mathematik

Descrizione articolo

Riassunto

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.

Dalla quarta di copertina

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 asa new chapter devoted to asymptotically optimal filtering under diffusion approximation. Moreover, in each chapter a comment is added about the progress of recent years.