Robert S Liptser

(Author)

Statistics of Random Processes II: ApplicationsPaperback, 15 December 2010

Statistics of Random Processes II: Applications
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Part of Series
Stochastic Modelling and Applied Probability
Print Length
402 pages
Language
English
Publisher
Springer
Date Published
15 Dec 2010
ISBN-10
364208365X
ISBN-13
9783642083655

Description

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.

Product Details

Authors:
Robert S LiptserAlbert N Shiryaev
Book Format:
Paperback
Country of Origin:
NL
Date Published:
15 December 2010
Dimensions:
23.39 x 15.6 x 2.18 cm
ISBN-10:
364208365X
ISBN-13:
9783642083655
Language:
English
Location:
Berlin, Heidelberg
Pages:
402
Publisher:
Weight:
585.13 gm

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