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Titlebook: Stochastic Filtering Theory; Gopinath Kallianpur Book 1980 Springer-Verlag New York 1980 Filtering.Filterung.Martingale.Prädiktion.STATIST

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发表于 2025-3-21 16:05:47 | 显示全部楼层 |阅读模式
书目名称Stochastic Filtering Theory
编辑Gopinath Kallianpur
视频video
丛书名称Stochastic Modelling and Applied Probability
图书封面Titlebook: Stochastic Filtering Theory;  Gopinath Kallianpur Book 1980 Springer-Verlag New York 1980 Filtering.Filterung.Martingale.Prädiktion.STATIST
描述This book is based on a seminar given at the University of California at Los Angeles in the Spring of 1975. The choice of topics reflects my interests at the time and the needs of the students taking the course. Initially the lectures were written up for publication in the Lecture Notes series. How­ ever, when I accepted Professor A. V. Balakrishnan‘s invitation to publish them in the Springer series on Applications of Mathematics it became necessary to alter the informal and often abridged style of the notes and to rewrite or expand much of the original manuscript so as to make the book as self-contained as possible. Even so, no attempt has been made to write a comprehensive treatise on filtering theory, and the book still follows the original plan of the lectures. While this book was in preparation, the two-volume English translation of the work by R. S. Liptser and A. N. Shiryaev has appeared in this series. The first volume and the present book have the same approach to the sub­ ject, viz. that of martingale theory. Liptser and Shiryaev go into greater detail in the discussion of statistical applications and also consider inter­ polation and extrapolation as well as filtering.
出版日期Book 1980
关键词Filtering; Filterung; Martingale; Prädiktion; STATISTICA; filtering problem; stochastic process
版次1
doihttps://doi.org/10.1007/978-1-4757-6592-2
isbn_softcover978-1-4419-2810-8
isbn_ebook978-1-4757-6592-2Series ISSN 0172-4568 Series E-ISSN 2197-439X
issn_series 0172-4568
copyrightSpringer-Verlag New York 1980
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发表于 2025-3-21 23:33:01 | 显示全部楼层
The Ito Formula, each . = 1, ... ,., or equivalently, if (.,..,) is a real-valued martingale with respect to (..) for every ., ∈ ... Here we use (,) to denote inner product in ... (.., ..) with .. = 0 (a.s.) is a .-dimensional, continuous ..-martingale if for every . ∈ .., (.,... is a continuous ..-martingale with
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The General Filtering Problem and the Stochastic Equation of the Optimal Filter (Part I),on of the optimal filter which will be derived in the later sections of this chapter. Let us recall that (.) is a complete probability space and (..) (t ∈ ..) is an increasing family of sub σ-fields of ., and that it will be assumed that all .-null sets belong to ℱ.. The following processes are give
发表于 2025-3-22 10:25:54 | 显示全部楼层
Gaussian Solutions of Stochastic Equations,odel it has been seen that the observation process and the innovation (Wiener) process are connected by an equation of the kind studied in Chapter 8. When the observation process is Gaussian, we have an example of the equation which will now be considered. The theory of stochastic equations whose so
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发表于 2025-3-22 21:05:24 | 显示全部楼层
The Stochastic Equation of the Optimal Filter (Part II),.) for which the condition .is fulfilled. However, the filtering problem can be regarded as completely solved if we can derive from (8.4.22) a stochastic differential equation for the conditional probability distribution—or the condition probability density—of .. given, ℱ.. and if, furthermore, it c
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Stochastic Processes: Basic Concepts and Definitions,d in detail in well-known standard textbooks, such as P. A. Meyer’s book, . [41]. However, those proofs will be presented which are not available in existing books and are to be found scattered in the literature, or which discuss ideas specially relevant to our purpose.
发表于 2025-3-23 06:44:34 | 显示全部楼层
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