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Titlebook: Gaussian Random Processes; I. A. Ibragimov,Y. A. Rozanov Book 1978 Springer-Verlag New York Inc. 1978 Ergodic theory.Gaussian measure.Gaus

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樓主
發(fā)表于 2025-3-21 19:06:21 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
書目名稱Gaussian Random Processes
編輯I. A. Ibragimov,Y. A. Rozanov
視頻videohttp://file.papertrans.cn/381/380957/380957.mp4
叢書名稱Stochastic Modelling and Applied Probability
圖書封面Titlebook: Gaussian Random Processes;  I. A. Ibragimov,Y. A. Rozanov Book 1978 Springer-Verlag New York Inc. 1978 Ergodic theory.Gaussian measure.Gaus
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
關(guān)鍵詞Ergodic theory; Gaussian measure; Gaussscher Prozess; Station?rer Prozess; mixing; probability measure; ra
版次1
doihttps://doi.org/10.1007/978-1-4612-6275-6
isbn_softcover978-1-4612-6277-0
isbn_ebook978-1-4612-6275-6Series ISSN 0172-4568 Series E-ISSN 2197-439X
issn_series 0172-4568
copyrightSpringer-Verlag New York Inc. 1978
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沙發(fā)
發(fā)表于 2025-3-21 21:11:40 | 只看該作者
Book 1978absolute 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 process
板凳
發(fā)表于 2025-3-22 04:20:09 | 只看該作者
Autogenes Training und gestufte Aktivhypnoseion of . are completely analogous to the results obtained in Chapter V for processes with discrete time. Specific difficulties arise only in the case of .) as . → ∞; unfortunately, the investigation of this case is less complete, although Theorems 5 and 6 do give some idea about phenomena arising here (see Sections VI.5 and VI.6).
地板
發(fā)表于 2025-3-22 06:34:16 | 只看該作者
Complete Regularity and Processes with Continuous Time,ion of . are completely analogous to the results obtained in Chapter V for processes with discrete time. Specific difficulties arise only in the case of .) as . → ∞; unfortunately, the investigation of this case is less complete, although Theorems 5 and 6 do give some idea about phenomena arising here (see Sections VI.5 and VI.6).
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https://doi.org/10.1007/978-3-642-85705-8oduct of vectors .=(.,…,.)and . = (.,…,.)) has the form .where . = (.…, .) ∈ ? is the . and . is a linear self-adjoint non- negative definite operator called a .; the matrix {.}defining . is said to be a ..
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發(fā)表于 2025-3-23 00:54:37 | 只看該作者
https://doi.org/10.1007/978-3-662-00542-2s generated by the process on the set ., that is, . (.) is the minimal .-algebra containing events such as.the . being Borel sets on the real line.* Algebras of the form .(?∞, .) determine the past of the process (before time .), algebras of the form .(., ∞) determine the future of the process (after time .).
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Conditions for Regularity of Stationary Random Processes,s generated by the process on the set ., that is, . (.) is the minimal .-algebra containing events such as.the . being Borel sets on the real line.* Algebras of the form .(?∞, .) determine the past of the process (before time .), algebras of the form .(., ∞) determine the future of the process (after time .).
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