| 书目名称 | Statistics of Random Processes | | 副标题 | I. General Theory | | 编辑 | Robert S. Liptser,Albert N. Shiryaev | | 视频video | | | 概述 | 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 ad | | 丛书名称 | Stochastic Modelling and Applied Probability | | 图书封面 |  | | 描述 | 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 | | 出版日期 | Book 2001Latest edition | | 关键词 | Conditionally Gaussian; Filtering; Incomplete Data Control; Martingale; Observable; Point Process; Probabi | | 版次 | 2 | | doi | https://doi.org/10.1007/978-3-662-13043-8 | | isbn_softcover | 978-3-642-08366-2 | | isbn_ebook | 978-3-662-13043-8Series ISSN 0172-4568 Series E-ISSN 2197-439X | | issn_series | 0172-4568 | | copyright | Springer-Verlag Berlin Heidelberg 2001 |
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发表于 2025-3-21 17:06:38
