| 书目名称 | Gaussian Random Processes | | 编辑 | I. A. Ibragimov,Y. A. Rozanov | | 视频video | | | 丛书名称 | Stochastic Modelling and Applied Probability | | 图书封面 |  | | 描述 | The book deals mainly with three problems involving Gaussian stationary processes. The first problem consists of clarifying the conditions for mutual absolute continuity (equivalence) of probability distributions of a "random process segment" and of finding effective formulas for densities of the equiva lent distributions. Our second problem is to describe the classes of spectral measures corresponding in some sense to regular stationary processes (in par ticular, satisfying the well-known "strong mixing condition") as well as to describe the subclasses associated with "mixing rate". The third problem involves estimation of an unknown mean value of a random process, this random process being stationary except for its mean, i. e. , it is the problem of "distinguishing a signal from stationary noise". Furthermore, we give here auxiliary information (on distributions in Hilbert spaces, properties of sam ple functions, theorems on functions of a complex variable, etc. ). Since 1958 many mathematicians have studied the problem of equivalence of various infinite-dimensional Gaussian distributions (detailed and sys tematic presentation of the basic results can be found, for instance, | | 出版日期 | Book 1978 | | 关键词 | Ergodic theory; Gaussian measure; Gaussscher Prozess; Stationärer Prozess; mixing; probability measure; ra | | 版次 | 1 | | doi | https://doi.org/10.1007/978-1-4612-6275-6 | | isbn_softcover | 978-1-4612-6277-0 | | isbn_ebook | 978-1-4612-6275-6Series ISSN 0172-4568 Series E-ISSN 2197-439X | | issn_series | 0172-4568 | | copyright | Springer-Verlag New York Inc. 1978 |
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发表于 2025-3-21 19:06:21
