| 书目名称 | The Geometry of Filtering | | 编辑 | K. David Elworthy,Yves Le Jan,Xue-Mei Li | | 视频video | | | 概述 | Includes supplementary material: | | 丛书名称 | Frontiers in Mathematics | | 图书封面 |  | | 描述 | Filtering is the science of nding the law of a process given a partial observation of it. The main objects we study here are di usion processes. These are naturally associated with second-order linear di erential operators which are semi-elliptic and so introduce a possibly degenerate Riemannian structure on the state space. In fact, much of what we discuss is simply about two such operators intertwined by a smooth map, the projection from the state space to the observations space", and does not involve any stochastic analysis. From the point of view of stochastic processes, our purpose is to present and to study the underlying geometric structure which allows us to perform the ltering in a Markovian framework with the resulting conditional law being that of a Markov process which is time inhomogeneous in general. This geometry is determined by the symbol of the operator on the state space which projects to a symbol on the observation space. The projectible symbol induces a (possibly non-linear and partially de ned) connection which lifts the observation process to the state space and gives a decomposition of the operator on the state space and of the noise. As is standard we can r | | 出版日期 | Book 2010 | | 关键词 | diffeomorphism; diffusion operator; diffusion process; filtering; manifold; semigroup; stochastic flow | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-0346-0176-4 | | isbn_softcover | 978-3-0346-0175-7 | | isbn_ebook | 978-3-0346-0176-4Series ISSN 1660-8046 Series E-ISSN 1660-8054 | | issn_series | 1660-8046 | | copyright | Springer Basel AG 2010 |
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发表于 2025-3-21 16:15:32
