Statistics of Random Processes I: General Theory - Couverture rigide

Liptser, Robert S.; Shiryaev, Albert N.

Couverture rigide

ISBN 10 : 3540639292 ISBN 13 : 9783540639299

Editeur : Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 2000

Synopsis

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.

A propos du livre

Revue de presse

From the reviews:

JOURNAL OF THE AMERICAN STOCHASTIC ASSOCIATION

"The material is accessible to researchers and advanced graduate students. These two classic volumes are very important resources for both probabilists and statisticians."

SIAM REVIEW

"Written by two renowned experts in the field, the books under review contain a thorough and insightful treatment of the fundamental underpinnings of various aspects of stochastic processes as well as a wide range of applications. Providing clear exposition, deep mathematical results, and superb technical representation, they are masterpieces of the subject of stochastic analysis and nonlinear filtering...What is special about these books is their broad coverage and in-depth study of optimal filtering problems...The books can be used by researchers in different areas who need to use stochastic calculus and who treat state estimation, detection, and stochastic control problems under incomplete information and partial observations...These two books are a comprehensive treatise on stochastic calculus, random processes, and filtering theory, and provide an excellent and illuminating introduction to these fields with a wide range of theoretical and practical issues. With the new additions and modifications of the first edition, they are to be welcomed and benefit not only the systems theory and control community but also mathematicians working on stochastic processes; engineers in control, communication, and signal processing; researchers in financial engineering; and scientists in many other related fields. It is conceivable that these books will have a significant impact on the aforementioned fields and will become classics."

SIAM REVIEW

"The first volume of the books may also be used as an advanced graduate-level textbook for a course in stochastic processes..."

From the reviews of the second edition:

"This is the revised and expanded second edition of the first version in Russian of (1974) and in English (1997, 1978). The ambitious program of the authors was to give for the first time a systematic account of the stochastic calculus and the unifying power and efficiency of its methods for the study of statistics of random process. ... The very detailed exposition of the text will in particular appeal to the mathematically interested reader and scientist." (Metrika, July, 2002)

"For several reasons stochastic analysis has been among the scientific hits of the last few decades. ... The reference list is also updated with essential recently published papers and books. Thus the comprehensive content and the masterly written text make the book attractive for researchers in stochastic analysis and its applications as well as for graduate students in the area. ... this book will continue to be among the most useful and popular books on the subject in the decades to come." --(Jordan M. Stoyanov, Zentralblatt MATH, Issue 1008, 2003)

Présentation de l'éditeur

These volumes cover non-linear filtering (prediction and smoothing) theory and its applications to the problem of optimal estimation, control with incomplete data, information theory, and sequential testing of hypothesis. Also presented is the theory of martingales, of interest to those who deal with problems in financial mathematics. These editions include new material, expanded chapters, and comments on recent progress in the field.

Détails de l'édition

• Éditeur: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
• Date d'édition: 2000
• Langue: anglais
• ISBN 10: 3540639292
• ISBN 13: 9783540639299
• Reliure: Relié
• Numéro d'édition: 2
• Nombre de pages: 427
• Coordonnées du fabricant: non disponible
• Personne responsable: CMN Printpool Inh. Mathis Neumann; https://www.also.com/ec/cms5/en_6000/6000/index.jsp; ; Friedrich-Karl-Str. 9; Hamburg; Allemagne